HJM, Vol. 45, No. 1, 2019

HOUSTON JOURNAL OF MATHEMATICS

Electronic Edition Vol. 45, No. 1, 2019

Editors: D. Bao (San Francisco, SFSU), D. Blecher (Houston), B. G. Bodmann (Houston), H. Brezis (Paris and Rutgers), B. Dacorogna (Lausanne), K. Davidson (Waterloo), M. Dugas (Baylor), M. Gehrke (LIAFA, Paris7), C. Hagopian (Sacramento), A. Haynes (Houston), R. M. Hardt (Rice), Y. Hattori (Matsue, Shimane), W. B. Johnson (College Station), M. Rojas (College Station), Min Ru (Houston), S.W. Semmes (Rice).
Managing Editors: B. G. Bodmann and K. Kaiser (Houston)

Houston Journal of Mathematics

Contents

Ivon Vidal-Escobar, Centro de Ciencias Matemáticas UNAM, Campus Morelia Apartado Postal 61-3 (Xangari) C.P. 58089, Morelia, Michoacán, MEXICO (paula@matmor.unam.mx)
Properties of the shift map on dendrites that are generalized inverse limits, pp. 1-19.
ABSTRACT. Given a closed subset M of [0,1]×[0,1], we will denote the generalized inverse limit of M by X and the shift map of X to X by σ. In this paper we show that if X is a hereditarily arc-wise connected continuum with a finite number of ramification points, then σ restricted to the set of ramification points is a permutation. Furthermore if X is a dendrite, then each ramification point of X has period 1 or 2 under σ.

Jorge Picado, CMUC, Department of Mathematics, University of Coimbra, 3001-501 Coimbra, Portugal (picado@mat.uc.pt), Aleš Pultr, Department of Applied Mathematics and ITI, MFF, Charles University, Malostranské nám. 24, 11800 Praha 1, Czech Republic (pultr@kam.mff.cuni.cz), and Anna Tozzi, Department of Mathematics, Università degli Studi dell'Aquila, Via Vetoio, 67160 Coppito (AQ), Italy (anna.tozzi@univaq.it).
Joins of closed sublocales, pp. 21-38.
ABSTRACT. Sublocales that are joins of closed ones constitute a frame S_⋁𝔠(L) embedded as a sup-sublattice into the coframe S(L) of sublocales of L. We prove that in the case of subfit L it is a subcolocale of S(L), that it is then a Boolean algebra and in fact precisely the Booleanization of S(L). In case of a T₁-space X, S_⋁𝔠(Ω(X)) picks precisely the sublocales corresponding to induced subspaces. In linear L and more generally if L is also a coframe, S_⋁𝔠(L) is both a frame and a coframe, but with trivial exceptions not Boolean and not a subcolocale of S(L).

Mohamed Ali, Toumi, Université de Carthage, Faculté des Sciences de Bizerte, Département des Mathématiques, 7021 Zarzouna, Bizerte, Tunisia, (MohamedAli.Toumi@fsb.rnu.tn).
Dedekind complete unital f-algebras on which every band preserving operator is order bounded, pp. 39-54
ABSTRACT. We give a complete description of those Dedekind complete unital f-algebras A with the property that every band preserving operator on A is order bounded. As an application, we furnish a new characterization of locally one dimensional universally complete vector lattices.

Behnam Khosravi, Department of Mathematics, Institute for Advanced Studies in Basic Sciences, Zanjan 45137-66731, Iran, (behnam_kho@yahoo.com), Behrooz Khosravi, Dept. of Pure Math., Faculty of Math. and Computer Sci. Amirkabir University of Technology (Tehran Polytechnic) 424, Hafez Ave., Tehran 15914, Iran, (khosravibbb@yahoo.com), and Bahman Khosravi, Department of Mathematics, Qom University of Technology, Qom, Iran, (khosravibahman@yahoo.com).
On Vertex-transitive Cayley graphs of semigroups and groups , pp. 55-69.
ABSTRACT. In this paper, first we show that for every monoid S, if every element of a subset C Í S has finitely many right inverses, then G=Cay(S,C) is ColAut_C(S)-vertex-transitive if and only if G is a group graph. Then we present a constructive example of a monoid S and a subset C Í S such that Cay(S,C) is ColAut_C(S)-vertex-transitive but it is not a group graph. So we show that the family of vertex-transitive graphs properly contains the family of automorphism vertex-transitive Cayley graphs of semigroups, and the later properly contains the family of Cayley graphs of groups

Jin-Lin, Liu, Department of Mathematics, Yangzhou University,Yangzhou 225002, P. R. China (jlliu@yzu.edu.cn).
Applications of differential subordinations for generalized Bessel functions, pp. 71-85.
ABSTRACT. Some novel applications of differential subordination for multivalent analytic functions with an operator involving generalized Bessel functions are given.

Hyungwoon Koo, Department of Mathematics, Korea University, Seoul 136-713, KOREA (koohw@korea.ac.kr) and Song-Ying Li, Department of Mathematics, University of California, Irvine, CA 92697-3875} (sli@math.uci.edu).
Composition operator on finite type model domains and certain weighted Bergman spaces over the unit ball, pp. 87-114.
ABSTRACT. We give a characterization for the boundedness of a composition operator on the Bergman space over the two dimensional finite type model domains. For which, we study the boundedness of the composition operators on some singular weighted Bergman space over the two dimensional unit ball. We investigate composition operators on these singular weighted Bergman spaces over the unit ball with smooth symbols, and provide various interesting examples which reveal quite different phenomena from those on the usual weighted Bergman spaces over the unit ball.

Jun-Fan Chen, (Corresponding author) and Xiao-Hua Cai, Department of Mathematics, Fujian Normal University, Fuzhou 350117, P.R. China (junfanchen@163.com) (xhcai1992@163.com).
Uniqueness results of meromorphic functions with finite and noninteger order, pp. 115-127.
ABSTRACT. We prove a uniqueness result of meromorphic functions withfinite and noninteger order. Furthermore, some examples are provided to demonstrate that all the conditions are necessary.

Napier, Terrence, Lehigh University, Bethlehem, PA 18015 (tjn2@lehigh.edu), and Ramachandran, Mohan, University at Buffalo, Buffalo, NY 14260 (ramac-m@buffalo.edu).
Weakly special filtered ends of complete Kähler manifolds, proper holomorphic mappings to Riemann surfaces, and the Bochner-Hartogs dichotomy, pp. 129-173.
ABSTRACT. Results concerning the structure of connected noncompact complete Kähler manifolds with (filtered) ends of one of several possible weakly special types are considered. For example, an end for which there is a nonnegative continuous plurisubharmonic function on the manifold that is unbounded on the end and for which the manifold has bounded geometry along each level in the end is weakly special of type (LI). In particular, every end of a connected covering manifold of a connected noncompact weakly 1-complete complete Kähler manifold is of type (LI). It is shown that a connected noncompact complete Kähler manifold that admits a weakly special ends decomposition and has at least three weakly special filtered ends admits a proper holomorphic mapping onto a Riemann surface. It is also shown that the Bochner-Hartogs dichotomy holds for any one-ended connected complete Kähler with a weakly special end of type (LI); that is, either the first compactly supported cohomology with values in the structure sheaf vanishes, or there exists a proper holomorphic mapping onto a Riemann surface. From this it follows that the Bochner-Hartogs dichotomy holds for any one-ended connected covering space of a connected noncompact weakly 1-complete Kähler manifold. These results are obtained as applications of a version of Gromov's cup product lemma that the authors had obtained earlier and that appeared elsewhere.

Yang Jiang (corresponding author), College of Math and Systematic Science, Shenyang Normal University, Liaoning, China, 110034 (xjiangyang@126.com), and Shyuichi Izumiya, Department of Mathematics, Hokkaido University, Hokkaido,Japan,0600180 (izumiya@math.sci.hokudai.ac.jp).
Lightcone dualities for submanifolds in the sphere, pp. 175-199.
ABSTRACT. In this paper we consider the submanifolds in the lightcone unit sphere. The unit sphere can be canonically embedded in the lightcone and de Sitter (n+1)-space in the Lorentz-Minkowski space. We investigate these submanifolds in the framework of the theory of Legendrian dualities between pseudo-spheres in the Lorentz-Minkowski space. We compare these dualities with the classical duality of submanifolds in the Euclidean sphere.

Buck, Leah, Department of Mathematics and Computer Science, Muskingum University, 163 Stormont St., New Concord, OH 43762 (lbuck@muskingum.edu), Emmrich, Kelly, Department of Mathematics, University of Wisconsin - La Crosse, 1725 State St., La Crosse, WI 54601 (emmrich.kelly@uwlax.edu), Forgács, Tamás, Department of Mathematics, California State University, Fresno, 5245 N. Backer, M/S PB108, Fresno, CA 93740-8001 (tforgacs@csufresno.edu)
Sufficient conditions for a linear operator on ℝ[x] to be monotone, pp. 201-212.
ABSTRACT. We demonstrate that being a hyperbolicity preserver does not imply monotonicity for infinite order differential operators on ℝ[x], thereby settling a recent conjecture in the negative. We also give some sufficient conditions for such operators to be monotone.

Anna Kamińska, Department of Mathematical Sciences, The University of Memphis, TN 38152-3240 (kaminska@memphis.edu), Han Ju Lee, Department of Mathematical Education, Dongguk University - Seoul, Seoul, 100-715, Republic of Korea (hanjulee@dongguk.edu), and Hyung-Joon Tag, Department of Mathematical Sciences, The University of Memphis, TN 38152-3240 (hjtag4@gmail.com).
M-ideal properties in Orlicz-Lorentz spaces, pp. 213-232.
ABSTRACT. We provide explicit formulas for the norm of bounded linear functionals on Orlicz-Lorentz function spaces Λ_φ,w equipped with two standard Luxemburg and Orlicz norms. Any bounded linear functional is a sum of regular and singular functionals, and we show that the norm of a singular functional is the same regardless of the norm in the space, while the formulas of the norm of general functionals are different for the Luxemburg and Orlicz norm. The relationship between equivalent definitions of the modular P_φ,wgenerating the dual space to Orlicz-Lorentz space is discussed in order to compute the norm of a bounded linear functional on Λ_φ,w equipped with Orlicz norm. As a consequence, we show that the order-continuous subspace of Orlicz-Lorentz space equipped with the Luxemburg norm is an M-ideal in Λ_φ,w, while this is not true for the space with the Orlicz norm when φ is an Orlicz N-function not satisfying the appropriate Δ₂condition. The analogous results on Orlicz-Lorentz sequence spaces are given.

Zarikian, Vrej, United States Naval Academy, Annapolis, MD 21402 (zarikian@usna.edu).
The pure extension property for discrete crossed products, pp. 233-243.
ABSTRACT. Let G be a discrete group acting on a unital C*-algebra A by *-automorphisms. In this note, we show that the inclusion of A into its reduced crossed product by G has the pure extension property (so that every pure state on A extends uniquely to a pure state on the crossed product) if and only if G acts freely on the spectrum of A. The same characterization holds for the inclusion of A into its full crossed product by G. This generalizes what was already known for A abelian.

Yunwei Xia, School of Mathematics and Statistics,Southwest University, Chongqing 400715, China (xiayunw@swu.edu.cn)
Star body valued valuations on L^q-spaces, pp. 245-264.
ABSTRACT. All continuous GL(n) contravariant star body valued valuations on Lq-spaces are completely classified. A consequence is a new characterization of polar symmetric centroid bodies.

Chongxia Lu, Hunan University, Changsha, Hunan, 410082, P.R. China, Dexian Liu, Hunan University, Changsha, Hunan, 410082, P.R. China, and Qingguo Li, Hunan University, Changsha, Hunan, 410082, P.R. China (liqingguoli@aliyun.com).
Equality of the Isbell and Scott topologies on function spaces of c-spaces, pp. 265-284.
ABSTRACT. In this paper, we mainly consider the question of when the Isbell and Scott topologies coincide on the set [X→L] of all continuous mappings from a topological space X to a dcpo L with the pointwise order. The main results are: (1) If L is a weak sober dcpo which is bi-complete, then (i) that the Isbell and Scott topologies coincide on [X→L] for all c-spaces X implies that L is a pointed L-dcpo; (ii) that the Isbell and Scott topologies coincide on [X→L] for all irreducible c-spaces X implies that L is an L-dcpo. (2) Let L be a quasicontinuous UBC-domain and X a c-space. If L has a least element or X is connected, then the Isbell and Scott topologies coincide on [X→L]. (3) Let L be a quasicontinuous UFL-domain and the topological space X disjoint union of Xi, where every Xi is an irreducible Scott c-space, i∈I and I is a nonempty finite set. If L has a least element or I is a singleton, then the Isbell and Scott topologies coincide on [X→L].

Shijie Gu, Department of Mathematics, County College of Morris, Randolph, NJ, 07869 (sgu@ccm.edu)
On small metric spheres and local cone structures of Busemann G-spaces, pp. 285-291.
ABSTRACT. A G-space is a locally compact, complete geodesic space which has neighborhoods of bi-point uniqueness and in which geodesics are in finitely and uniquely extendable. It is shown that every sufficiently small metric sphere in n-dimensional (n<1) G-space is homotopy equivalent to the (n - 1)-sphere. We give a geometric obstruction to every sufficiently small metric ball in 4-dimensional G-space being a genuine 4-cell. We also prove that the Busemann conjecture is true if and only if every G-space is locally cone-like.

Shou Lin, Department of Mathematics, Ningde Normal University, Ningde, Fujian 352100, P.R. China (shoulin60@163.com) and Ying Ge, Department of Mathematics, Soochow University, Suzhou, Jiangsu 215006, P.R. China (geying@suda.edu.cn).
Compact-covering and 1-sequence-covering images of metric spaces, pp. 293-305.
ABSTRACT. In this paper, compact-covering and 1-sequence-covering images of metric spaces are investigates. By a Ponomarev's system, this paper characterizes sn-metrizable spaces by 1-sequence-covering, compact-covering and mssc-images of metric spaces, and it is proved that a space X has a point-star network consisting of locally finite sn-covers if and only if X is a sequence-covering, π and σ-image of a metric space. As an application of these results, this paper gives an affirmative answer to a question posed by P. Yan and S. Lin in Chinese Adv. Math.

Fernández, Leobardo Instituto Tecnológico Autónomo de México. Ciudad de México, México (leobardo.fernandez@itam.mx), Universidad Nacional Autónoma de México. Ciudad de México, México (leobardof@ciencias.unam.mx) and Puga, Isabel Universidad Nacional Autónoma de México. Ciudad de México, México (ispues@yahoo.com.mx)
On semi-Kelly continua, pp. 307-315.
ABSTRACT. Answering questions posted by J. J. Charatonik and W. J. Charatonik, in this paper it is proved that the property of being a semi-Kelley continuum is preserved under open mappings and under monotone mappings. Also, a not semi-confluent mapping f:X→Y, from a continuum X onto a continuum Y with the property of Kelley, which is the uniform limit of semi-confluent mappings from X onto Y is presented. In addition, we show that if a continuum X is a semi-Kelley continuum, then X does not contain R²-continua.

Nguyen Thi Nhung, Thang Long University, Vietnam (hoangnhung227@gmail.com) and Le Ngoc Quynh, An Giang University, Vietnam (nquynh1511@gmail.com) .
Corrigendum to "Unicity of meromorphic mappings from complete Kähler manifolds into projective spaces", pp. 317-320.