Weighted Spaces of Holomorphic Functions on Banach Spaces and the Approximation Property

In this paper, we study the linearization theorem for the weighted space Hw(U ; F ) of holomorphic functions defined on an open subset U of a Banach space E with values in a Banach space F. After having introduced a locally convex topology τM on the space Hw(U;F), we show that (Hw(U;F), τM) is topol...

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Main Authors:	Manjul Gupta, Deepika Baweja
Format:	Article
Language:	English
Published:	University of Extremadura 2016-12-01
Series:	Extracta Mathematicae
Subjects:	Holomorphic mappings weighted spaces of holomorphic functions linearization approximation property
Online Access:	https://publicaciones.unex.es/index.php/EM/article/view/391

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spelling	doaj-dd765dccc9d248ac902f54e42e083fb22021-02-02T17:22:33ZengUniversity of ExtremaduraExtracta Mathematicae0213-87432605-56862016-12-01312Weighted Spaces of Holomorphic Functions on Banach Spaces and the Approximation PropertyManjul Gupta0Deepika Baweja1Department of Mathematics and Statistics, IIT Kanpur, India - 208016Department of Mathematics and Statistics, IIT Kanpur, India - 208016In this paper, we study the linearization theorem for the weighted space Hw(U ; F ) of holomorphic functions defined on an open subset U of a Banach space E with values in a Banach space F. After having introduced a locally convex topology τM on the space Hw(U;F), we show that (Hw(U;F), τM) is topologically isomorphic to (L(Gw(U);F), τc) where Gw(U) is the predual of Hw(U) consisting of all linear functionals whose restrictions to the closed unit ball of Hw(U) are continuous for the compact open topology τ0 . Finally, these results have been used in characterizing the approximation property for the space Hw(U) and its predual for a suitably restricted weight w. https://publicaciones.unex.es/index.php/EM/article/view/391Holomorphic mappingsweighted spaces of holomorphic functionslinearizationapproximation property
collection	DOAJ
language	English
format	Article
sources	DOAJ
author	Manjul Gupta Deepika Baweja
spellingShingle	Manjul Gupta Deepika Baweja Weighted Spaces of Holomorphic Functions on Banach Spaces and the Approximation Property Extracta Mathematicae Holomorphic mappings weighted spaces of holomorphic functions linearization approximation property
author_facet	Manjul Gupta Deepika Baweja
author_sort	Manjul Gupta
title	Weighted Spaces of Holomorphic Functions on Banach Spaces and the Approximation Property
title_short	Weighted Spaces of Holomorphic Functions on Banach Spaces and the Approximation Property
title_full	Weighted Spaces of Holomorphic Functions on Banach Spaces and the Approximation Property
title_fullStr	Weighted Spaces of Holomorphic Functions on Banach Spaces and the Approximation Property
title_full_unstemmed	Weighted Spaces of Holomorphic Functions on Banach Spaces and the Approximation Property
title_sort	weighted spaces of holomorphic functions on banach spaces and the approximation property
publisher	University of Extremadura
series	Extracta Mathematicae
issn	0213-8743 2605-5686
publishDate	2016-12-01
description	In this paper, we study the linearization theorem for the weighted space Hw(U ; F ) of holomorphic functions defined on an open subset U of a Banach space E with values in a Banach space F. After having introduced a locally convex topology τM on the space Hw(U;F), we show that (Hw(U;F), τM) is topologically isomorphic to (L(Gw(U);F), τc) where Gw(U) is the predual of Hw(U) consisting of all linear functionals whose restrictions to the closed unit ball of Hw(U) are continuous for the compact open topology τ0 . Finally, these results have been used in characterizing the approximation property for the space Hw(U) and its predual for a suitably restricted weight w.
topic	Holomorphic mappings weighted spaces of holomorphic functions linearization approximation property
url	https://publicaciones.unex.es/index.php/EM/article/view/391
work_keys_str_mv	AT manjulgupta weightedspacesofholomorphicfunctionsonbanachspacesandtheapproximationproperty AT deepikabaweja weightedspacesofholomorphicfunctionsonbanachspacesandtheapproximationproperty
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Weighted Spaces of Holomorphic Functions on Banach Spaces and the Approximation Property

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