Cyclic Vectors in Banach Spaces of Analytic Functions

1985 ◽  
pp. 315-349 ◽  
Author(s):  
Allen L. Shields
Keyword(s):  
Banach Spaces ◽  
Analytic Functions ◽  
Cyclic Vectors ◽  
Spaces Of Analytic Functions

Essential Norm and Weak Compactness of Composition Operators on Weighted Banach Spaces of Analytic Functions

1999 ◽  
Vol 42 (2) ◽  
pp. 139-148 ◽  
Author(s):  
José Bonet ◽  
Paweł Dománski ◽  
Mikael Lindström
Keyword(s):  
Banach Space ◽  
Banach Spaces ◽  
Analytic Functions ◽  
Composition Operators ◽  
Essential Norm ◽  
Weak Compactness ◽  
Weakly Compact ◽  
Point Evaluation ◽  
Weighted Banach Spaces ◽  
Spaces Of Analytic Functions

AbstractEvery weakly compact composition operator between weighted Banach spaces of analytic functions with weighted sup-norms is compact. Lower and upper estimates of the essential norm of continuous composition operators are obtained. The norms of the point evaluation functionals on the Banach space are also estimated, thus permitting to get new characterizations of compact composition operators between these spaces.

Invariant subspaces of given index in Banach spaces of analytic functions

1998 ◽  
Vol 1998 (505) ◽  
pp. 23-44 ◽  
Author(s):  
Alexander Borichev
Keyword(s):  
Banach Spaces ◽  
Wide Class ◽  
Analytic Functions ◽  
Unit Disc ◽  
Bergman Spaces ◽  
Invariant Subspaces ◽  
Weighted Bergman Spaces ◽  
Common Zeros ◽  
Spaces Of Analytic Functions

Abstract For a wide class of Banach spaces of analytic functions in the unit disc including all weighted Bergman spaces with radial weights and for weighted ℓAp spaces we construct z-invariant subspaces of index n, 2 ≦ n ≦ + ∞, without common zeros in the unit disc.

scholarly journals Biduals of weighted banach spaces of analytic functions

1993 ◽  
Vol 54 (1) ◽  
pp. 70-79 ◽  
Author(s):  
K. D. Bierstedt ◽  
W. H. Summers
Keyword(s):  
Unit Ball ◽  
Banach Spaces ◽  
Open Subset ◽  
Analytic Functions ◽  
Holomorphic Functions ◽  
Supremum Norm ◽  
Closed Unit Ball ◽  
Weighted Banach Spaces ◽  
Spaces Of Analytic Functions ◽  
Continuous Weight

AbstractFor a positive continuous weight function ν on an open subset G of CN, let Hv(G) and Hv0(G) denote the Banach spaces (under the weighted supremum norm) of all holomorphic functions f on G such that ν f is bounded and ν f vanishes at infinity, respectively. We address the biduality problem as to when Hν(G) is naturally isometrically isomorphic to Hν0(G)**, and show in particular that this is the case whenever the closed unit ball in Hν0(G) in compact-open dense in the closed unit ball of Hν(G).

scholarly journals On M-ideals and o-O type spaces

2017 ◽  
Vol 121 (1) ◽  
pp. 151 ◽  
Author(s):  
Karl-Mikael Perfekt
Keyword(s):  
Banach Spaces ◽  
Analytic Functions ◽  
Function Spaces ◽  
Weighted Spaces ◽  
Bounded Mean Oscillation ◽  
Mean Oscillation ◽  
Type Spaces ◽  
Invariant Spaces ◽  
Holder Spaces ◽  
Spaces Of Analytic Functions

We consider pairs of Banach spaces $(M_0, M)$ such that $M_0$ is defined in terms of a little-$o$ condition, and $M$ is defined by the corresponding big-$O$ condition. The construction is general and pairs include function spaces of vanishing and bounded mean oscillation, vanishing weighted and weighted spaces of functions or their derivatives, Möbius invariant spaces of analytic functions, Lipschitz-Hölder spaces, etc. It has previously been shown that the bidual $M_0^{**}$ of $M_0$ is isometrically isomorphic with $M$. The main result of this paper is that $M_0$ is an M-ideal in $M$. This has several useful consequences: $M_0$ has Pełczýnskis properties (u) and (V), $M_0$ is proximinal in $M$, and $M_0^*$ is a strongly unique predual of $M$, while $M_0$ itself never is a strongly unique predual.

Sign in / Sign up

Export Citation Format

Share Document