Related papers: Weighted holomorphic mappings associated with p-co…
Let C be a nonempty closed convex subset of a real normed linear space $E$ and u, v are positive numbers. In this paper we introduce some new definitions that generalize the analogue definitions from real Hilbert spaces to real normed…
We study the approximation numbers of weighted composition operators $f\mapsto w\cdot(f\circ\varphi)$ on the Hardy space $H^2$ on the unit disc. For general classes of such operators, upper and lower bounds on their approximation numbers…
The numerical range of holomorphic mappings arises in many aspects of nonlinear analysis, finite and infinite dimensional holomorphy, and complex dynamical systems. In particular, this notion plays a crucial role in establishing exponential…
For a fixed Banach operator ideal $\mathcal A$, we use the notion of $\mathcal A$-compact sets of Carl and Stephani to study $\mathcal A$-compact polynomials and $\mathcal A$-compact holomorphic mappings. Namely, those mappings $g\colon…
We construct a compact linearly ordered space $K$ of weight aleph one, such that the space $C(K)$ is not isomorphic to a Banach space with a projectional resolution of the identity, while on the other hand, $K$ is a continuous image of a…
For a K\"{a}hler manifold endowed with a weighted measure $e^{-f}\,dv,$ the associated weighted Hodge Laplacian $\Delta _{f}$ maps the space of $(p,q)$-forms to itself if and only if the $(1,0)$-part of the gradient vector field $\nabla f$…
A necessary and sufficient condition for an operator space to support a multiplication making it completely isometric and isomorphic to a unital operator algebra is proved. The condition involves only the holomorphic structure of the Banach…
We consider weighted composition operators on spaces of analytic functions on the unit disc, which take values in some complex Banach space. We provide necessary and sufficient conditions for the boundedness and (weak) compactness of…
Weighted EP Banach space operators and Banach algebra elements are characterized using different kinds of factorizations. The results presented extend well-known characterizations of (weighted) EP matrices, (weighted) EP Hilbert space…
We show that the duals of Banach algebras of scalar-valued bounded holomorphic functions on the open unit ball $B_E$ of a Banach space $E$ lack weak$^*$-strongly exposed points. Consequently, we obtain that some Banach algebras of…
We study the interaction between various analytification functors, and a class of morphisms of rings, called homotopy epimorphisms. An analytification functor assigns to a simplicial commutative algebra over a ring $R$, along with a choice…
The authors lay the foundations for the study of normal families of holomorphic functions and mappings on an infinite-dimensional normed linear space. Characterizations of normal families, in terms of value distribution, spherical…
Let $V\subseteq W$ be two operator spaces. Arveson-Wittstock-Hahn-Banach theorem asserts that every completely contractive map $\varphi:V\to \mathcal{B}(H)$ has a completely contractive extension $\tilde{\varphi}:W\to \mathcal{B}(H)$, where…
We give a criterion ensuring that the elementary class of a modular Banach space E (that is, the class of Banach spaces, some ultrapower of which is linearly isometric to an ultrapower of E) consists of all direct sums E\oplus_m H, where H…
Many of the known complemented subspaces of L_p have realizations as sequence spaces. In this paper a systematic approach to defining these spaces which uses partitions and weights is introduced. This approach gives a unified description of…
We study a "$p$-powered" version $K_n^p(F(R))$ of the well-known Bohr radius problem for the family $F(R)$ of holomorphic functions $f: R\to X$ satisfying $\|f\|<\infty$, where $\|.\|$ is a norm in the function space $F(R)$,…
We discuss the continuity of the composition on several spaces of holomorphic mappings on open subsets of a complex Banach space. On the Fr\'{e}chet space of the entire mappings that are bounded on bounded sets the composition turns to be…
We characterize boundedness, compactness and weak compactness of Volterra operators acting between different weighted Banach spaces of entire functions with weighted sup-norms in terms of the symbol g. Thus we complement recent work by…
This paper is concerned with the study of geometric structures in spaces of polynomials. More precisely, we discuss for $E$ and $F$ Banach spaces, whether the class of weakly continuous on bounded sets $n$-homogeneous polynomials, $\mathcal…
In this article, we show that the predual $\mathcal{G}_w(U)$ of the weighted space of holomorphic functions has the $\mathcal{I}$- approximation property if and only if $E$ has the $\mathcal{I}$- approximation property, where $\mathcal{I}$…