Shrinking and boundedly complete Schauder frames in Frechet spaces

被引：5

作者：

Bonet, Jose ^{[1
]}

Fernandez, Carmen ^{[2
]}

Galbis, Antonio ^{[2
]}

Ribera, Juan M. ^{[1
]}

机构：

[1] Univ Politecn Valencia, Inst Univ Matemat Pura & Aplicada IUMPA, E-46071 Valencia, Spain

[2] Univ Valencia, Dept Anal Matemat, E-46100 Valencia, Spain

来源：

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS | 2014年 / 410卷 / 02期

关键词：

Atomic decomposition; Schauder basis; Schauder frame; Frechet spaces; (LB)-spaces; Reflexivity; Locally convex spaces; Shrinking; Boundedly complete; INTEGRABLE GROUP-REPRESENTATIONS; LOCALLY CONVEX-SPACES; BANACH-SPACES; ATOMIC DECOMPOSITIONS; APPROXIMATION PROPERTY; COMPLEMENTED SUBSPACE; EXPANSIONS; REGULARITY; SEQUENCES; OPERATORS;

D O I：

10.1016/j.jmaa.2013.09.010

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We study Schauder frames in Frechet spaces and their duals, as well as perturbation results. We define shrinking and boundedly complete Schauder frames on a locally convex space, study the duality of these two concepts and their relation with the reflexivity of the space. we characterize when an unconditional Schauder frame is shrinking or boundedly complete in terms of properties of the space. Several examples of concrete Schauder frames in function spaces are also presented. (C) 2013 Elsevier Inc. All rights reserved.

引用

页码：953 / 966

页数：14

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