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Search: MSC category 46E40 ( Spaces of vector- and operator-valued functions )

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1. CMB 2013 (vol 57 pp. 364)

Li, Lei; Wang, Ya-Shu
 How Lipschitz Functions Characterize the Underlying Metric Spaces Let $X, Y$ be metric spaces and $E, F$ be Banach spaces. Suppose that both $X,Y$ are realcompact, or both $E,F$ are realcompact. The zero set of a vector-valued function $f$ is denoted by $z(f)$. A linear bijection $T$ between local or generalized Lipschitz vector-valued function spaces is said to preserve zero-set containments or nonvanishing functions if $z(f)\subseteq z(g)\quad\Longleftrightarrow\quad z(Tf)\subseteq z(Tg),$ or $z(f) = \emptyset\quad \Longleftrightarrow\quad z(Tf)=\emptyset,$ respectively. Every zero-set containment preserver, and every nonvanishing function preserver when $\dim E =\dim F\lt +\infty$, is a weighted composition operator $(Tf)(y)=J_y(f(\tau(y)))$. We show that the map $\tau\colon Y\to X$ is a locally (little) Lipschitz homeomorphism. Keywords:(generalized, locally, little) Lipschitz functions, zero-set containment preservers, biseparating mapsCategories:46E40, 54D60, 46E15

2. CMB 2010 (vol 53 pp. 466)

Dubarbie, Luis
 Separating Maps between Spaces of Vector-Valued Absolutely Continuous Functions In this paper we give a description of separating or disjointness preserving linear bijections on spaces of vector-valued absolutely continuous functions defined on compact subsets of the real line. We obtain that they are continuous and biseparating in the finite-dimensional case. The infinite-dimensional case is also studied. Keywords:separating maps, disjointness preserving, vector-valued absolutely continuous functions, automatic continuityCategories:47B38, 46E15, 46E40, 46H40, 47B33

3. CMB 2004 (vol 47 pp. 49)

Lindström, Mikael; Makhmutov, Shamil; Taskinen, Jari
 The Essential Norm of a Bloch-to-$Q_p$ Composition Operator The $Q_p$ spaces coincide with the Bloch space for $p>1$ and are subspaces of $\BMOA$ for $0 Keywords:Bloch space, little Bloch space,$\BMOA$,$\VMOA$,$Q_p$spaces,, composition operator, compact operator, essential normCategories:47B38, 47B10, 46E40, 46E15 4. CMB 1999 (vol 42 pp. 118) Rao, T. S. S. R. K.  Points of Weak$^\ast$-Norm Continuity in the Unit Ball of the Space$\WC(K,X)^\ast$For a compact Hausdorff space with a dense set of isolated points, we give a complete description of points of weak$^\ast$-norm continuity in the dual unit ball of the space of Banach space valued functions that are continuous when the range has the weak topology. As an application we give a complete description of points of weak-norm continuity of the unit ball of the space of vector measures when the underlying Banach space has the Radon-Nikodym property. Keywords:Points of weak$^\ast$-norm continuity, space of vector valued weakly continuous functions,$M\$-idealsCategories:46B20, 46E40