An operator representation for weighted spaces of vector valued holomorphic functions

1999 ◽  
Vol 36 (1-2) ◽  
pp. 9-20 ◽  
Author(s):  
Klaus D. Bierstedt ◽  
Silke Holtmanns
Keyword(s):  
Holomorphic Functions ◽  
Weighted Spaces ◽  
Operator Representation ◽  
Vector Valued

scholarly journals Strict density inequalities for sampling and interpolation in weighted spaces of holomorphic functions

2019 ◽  
Vol 277 (12) ◽  
pp. 108282 ◽  
Author(s):  
Karlheinz Gröchenig ◽  
Antti Haimi ◽  
Joaquim Ortega-Cerdà ◽  
José Luis Romero
Keyword(s):  
Holomorphic Functions ◽  
Weighted Spaces ◽  
Spaces Of Holomorphic Functions

Composition operators on weighted spaces of holomorphic functions on the upper half plane

2018 ◽  
Vol 122 (1) ◽  
pp. 141
Author(s):  
Wolfgang Lusky
Keyword(s):  
Half Plane ◽  
Composition Operator ◽  
Unit Disc ◽  
Composition Operators ◽  
Bounded Operator ◽  
Holomorphic Functions ◽  
Weighted Spaces ◽  
Weight Functions ◽  
Spaces Of Holomorphic Functions ◽  
Upper Half Plane

We consider moderately growing weight functions $v$ on the upper half plane $\mathbb G$ called normal weights which include the examples $(\mathrm{Im} w)^a$, $w \in \mathbb G$, for fixed $a > 0$. In contrast to the comparable, well-studied situation of normal weights on the unit disc here there are always unbounded composition operators $C_{\varphi }$ on the weighted spaces $Hv(\mathbb G)$. We characterize those holomorphic functions $\varphi \colon \mathbb G \rightarrow \mathbb G$ where the composition operator $C_{\varphi } $ is a bounded operator $Hv(\mathbb G) \rightarrow Hv(\mathbb G)$ by a simple property which depends only on $\varphi $ but not on $v$. Moreover we show that there are no compact composition operators $C_{\varphi }$ on $Hv(\mathbb G)$.

Vector-valued holomorphic functions revisited

2000 ◽  
Vol 234 (4) ◽  
pp. 777-805 ◽  
Author(s):  
W. Arendt ◽  
N. Nikolski
Keyword(s):  
Holomorphic Functions ◽  
Vector Valued

scholarly journals On weak approximation and convexification in weighted spaces of vector-valued continuous functions

1989 ◽  
Vol 31 (1) ◽  
pp. 59-64 ◽  
Author(s):  
Marek Nawrocki
Keyword(s):  
Hausdorff Space ◽  
Continuous Functions ◽  
Weighted Spaces ◽  
Weak Approximation ◽  
Completely Regular ◽  
Hausdorff Topological Vector Space ◽  
The Family ◽  
Image Position ◽  
Positive Functions ◽  
Vector Valued

Let X be a completely regular Hausdorff space. A Nachbin family of weights is a set V of upper-semicontinuous positive functions on X such that if u, υ ∈ V then there exists w ∈ V and t > 0 so that u, υ ≤ tw. For any Hausdorff topological vector space E, the weighted space CV0(X, E) is the space of all E-valued continuous functions f on X such that υf vanishes at infinity for all υ ∈ V. CV0(X, E) is equipped with the weighted topologywv = wv(X, E) which has as a base of neighbourhoods of zero the family of all sets of the formwhere υ ∈ Vand W is a neighbourhood of zero in E. If E is the scalar field, then the space CV0(X, E) is denoted by CV0(X). The reader is referred to [4, 6, 8] for information on weighted spaces.

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