scholarly journals The approximation property for spaces of holomorphic functions on infinite dimensional spaces II

2010 ◽  
Vol 259 (2) ◽  
pp. 545-560 ◽  
Author(s):  
Seán Dineen ◽  
Jorge Mujica
Keyword(s):  
Approximation Property ◽  
Holomorphic Functions ◽  
Infinite Dimensional ◽  
Spaces Of Holomorphic Functions

scholarly journals Every Separable Complex Fréchet Space with a Continuous Norm is Isomorphic to a Space of Holomorphic Functions

2020 ◽  
pp. 1-5
Author(s):  
José Bonet
Keyword(s):  
Complex Plane ◽  
Unit Disc ◽  
Holomorphic Functions ◽  
Fréchet Space ◽  
Dense Subspace ◽  
Frechet Space ◽  
Fréchet Spaces ◽  
Continuous Norm ◽  
Infinite Dimensional ◽  
Spaces Of Holomorphic Functions

Abstract Extending a result of Mashreghi and Ransford, we prove that every complex separable infinite-dimensional Fréchet space with a continuous norm is isomorphic to a space continuously included in a space of holomorphic functions on the unit disc or the complex plane, which contains the polynomials as a dense subspace. As a consequence, we deduce the existence of nuclear Fréchet spaces of holomorphic functions without the bounded approximation.

HOLOMORPHIC SUPERPOSITION OPERATORS BETWEEN BANACH FUNCTION SPACES

2013 ◽  
Vol 96 (2) ◽  
pp. 186-197 ◽  
Author(s):  
CHRISTOPHER BOYD ◽  
PILAR RUEDA
Keyword(s):  
Large Class ◽  
Holomorphic Functions ◽  
Function Spaces ◽  
Weighted Spaces ◽  
Banach Function Spaces ◽  
Infinite Dimensional ◽  
Spaces Of Holomorphic Functions ◽  
Infinite Dimensional Holomorphy ◽  
Superposition Operators ◽  
Alpha Beta

AbstractWe prove that for a large class of Banach function spaces continuity and holomorphy of superposition operators are equivalent and that bounded superposition operators are continuous. We also use techniques from infinite dimensional holomorphy to establish the boundedness of certain superposition operators. Finally, we apply our results to the study of superposition operators on weighted spaces of holomorphic functions and the $F(p, \alpha , \beta )$ spaces of Zhao. Some independent properties on these spaces are also obtained.

scholarly journals Traces of certain classes of holomorphic functions on finite unions of Carleson sequences

1999 ◽  
Vol 41 (1) ◽  
pp. 103-114 ◽  
Author(s):  
ANDREAS HARTMANN
Keyword(s):  
Holomorphic Functions ◽  
Spaces Of Holomorphic Functions ◽  
Hardy Classes ◽  
Type Spaces ◽  
Trace Spaces

We give a method allowing the generalization of the description of trace spaces of certain classes of holomorphic functions on Carleson sequences to finite unions of Carleson sequences. We apply the result to different classes of spaces of holomorphic functions such as Hardy classes and Bergman type spaces.

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