*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*

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.

Joins of closed sublocales, pp. 21-38.

ABSTRACT. Sublocales that are joins of closed ones constitute a frame S

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.

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

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.

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.

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.

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

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.

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.

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

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.

Star body valued valuations on L

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.

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

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.

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.

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.

Corrigendum to "Unicity of meromorphic mappings from complete Kähler manifolds into projective spaces", pp. 317-320.