Related papers: p-Summing Bloch mappings on the complex unit disc

We study several classes of Banach bimodules over a II$_1$ factor $M$, endowed with topologies that make them "smooth" with respect to $L^p$-norms implemented by the trace on $M$. Letting $M\subset \B= \B(L^2M)$, and $2\leq p < \infty$, we…

The concept of uniform convexity of a Banach space was generalized to linear operators between Banach spaces and studied by Beauzamy [1976]. Under this generalization, a Banach space X is uniformly convex if and only if its identity map I_X…

We consider weighted Bergman projection $P_{\alpha}: L^{\infty}(\Bbb B) \rightarrow {\cal B} $ where $\alpha>-1$ and $\cal B$ is the Bloch space of the unit ball $\Bbb B$ of the complex space $\Bbb C^n.$ We obtain the exact norm of the…

We study the bounded and the compact weighted composition operators from the Bloch space into the weighted Banach spaces of holomorphic functions on bounded homogeneous domains, with particular attention to the unit polydisk. For bounded…

In this paper we prove a Schwarz-Pick lemma for the modulus of holomorphic mappings from the polydisk into the unit ball. This result extends some related results.

In 1994, M. M. Popov [On integrability in F-spaces, Studia Math. no 3, 205-220] showed that the fundamental theorem of calculus fails, in general, for functions mapping from a compact interval of the real line into the lp-spaces for 0<p<1,…

A Banach symmetric space in the sense of O. Loos is a smooth Banach manifold $M$ endowed with a multiplication map $\mu\colon M \times M \to M$ such that each left multiplication map $\mu_x := \mu(x,\cdot)$ (with $x \in M$) is an involutive…

Suppose $w$ is a sense-preserving harmonic mapping of the unit disk $\mathbb{D}$ such that $w(\mathbb{D})\subseteq\mathbb{D}$ and $w$ has a zero of order $p\geq1$ at $z=0$. In this paper, we first improve the Schwarz lemma for $w$, and…

The main result of the paper: Given any $\varepsilon>0$, every locally finite subset of $\ell_2$ admits a $(1+\varepsilon)$-bilipschitz embedding into an arbitrary infinite-dimensional Banach space. The result is based on two results which…

We introduce kernel-summability methods in Banach spaces using the vector-valued integrals and prove an analogue of the Silverman-Toeplitz Theorem for regular kernel-summability methods. We also show that if $X$ is a Banach space and one…

It is well known in convex analysis that proximal mappings on Hilbert spaces are $1$-Lipschitz. In the present paper we show that proximal mappings on uniformly convex Banach spaces are uniformly continuous on bounded sets. Moreover, we…

We provide a sufficient condition for the sum of a finite number of complemented subspaces of a Banach space to be complemented. Under this condition a formula for a projection onto the sum is given. We also show that the condition is sharp…

Given an open subset $U$ of a complex Banach space $E$, a weight $v$ on $U$, and a complex Banach space $F$, let $\mathcal{H}^\infty_v(U,F)$ denote the Banach space of all weighted holomorphic mappings $f\colon U\to F$, under the weighted…

The space of Bloch functions on bounded symmetric domains is extended by considering Bloch functions $f$ on the unit ball $B_E$ of finite and infinite dimensional complex Banach spaces in two different ways: by extending the classical Bloch…

We obtain a sharp estimate on the norm of the differential of a harmonic map from the unit disc $\mathbb D$ in $\mathbb C$ into the unit ball $\mathbb B^n$ in $\mathbb R^n$, $n\ge 2$, at any point where the map is conformal. In dimension…

We continue to investigate cases when the Repov\v{s}-Semenov splitting problem for selections has an affirmative solution for continuous set-valued mappings. We consider the situation in infinite-dimensional uniformly convex Banach spaces.…

We give a class of bounded closed sets $C$ in a Banach space satisfying a generalized and stronger form of the Bishop-Phelps property studied by Bourgain in \cite{Bj} for dentable sets. A version of the {\it ``Bishop-Phelps-Bollob\'as"}…

In this note we obtain new coincidence theorems for absolutely summing multilinear mappings between Banach spaces. We also prove that our results, in general, can not be improved.

We give a sufficient criterion for complex analyticity of nonlinear maps defined on direct limits of normed spaces. This tool is then used to construct new classes of (real and complex) infinite dimensional Lie groups: (a) groups of germs…

We show that there are sampling projections on arbitrary $n$-dimensional subspaces of $B(D)$ with at most $2n$ samples and norm of order $\sqrt{n}$, where $B(D)$ is the space of complex-valued bounded functions on a set $D$. This gives a…