The approximation property for spaces of holomorphic functions on infinite dimensional spaces III
Let denote the vector space of all complex-valued holomorphic functions on an open subset U of a Banach space E , with the Nachbin compact-ported topology. Let denote the vector space of all complex-valued holomorphic germs on a compact subset K of E , with its natural inductive limit topology. Let...
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| Vydané v: | Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A, Matemáticas Ročník 106; číslo 2; s. 457 - 469 |
|---|---|
| Hlavní autori: | , |
| Médium: | Journal Article |
| Jazyk: | English |
| Vydavateľské údaje: |
Milan
Springer Milan
01.09.2012
Springer Nature B.V |
| Predmet: | |
| ISSN: | 1578-7303, 1579-1505 |
| On-line prístup: | Získať plný text |
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| Shrnutí: | Let
denote the vector space of all complex-valued holomorphic functions on an open subset
U
of a Banach space
E
, with the Nachbin compact-ported topology. Let
denote the vector space of all complex-valued holomorphic germs on a compact subset
K
of
E
, with its natural inductive limit topology. Let
denote the Banach space of all continuous complex-valued
m
-homogeneous polynomials on
E
. When
E
has a Schauder basis, we show that
has the approximation property for every compact subset
K
of
E
if and only if
has the approximation property for every
. When
E
has an unconditional Schauder basis, we show that
has the approximation property for every pseudoconvex open subset
U
of
E
if and only if
has the approximation property for every
. These theorems apply in particular to the classical Banach spaces
and
, and to the original Tsirelson space
. |
|---|---|
| Bibliografia: | SourceType-Scholarly Journals-1 ObjectType-Feature-1 content type line 14 ObjectType-Article-2 content type line 23 |
| ISSN: | 1578-7303 1579-1505 |
| DOI: | 10.1007/s13398-012-0065-7 |