HILBERT-SCHAUDER FRAME OPERATORS

被引：5

作者：

Liu, Rui ^{[1
,2
]}

机构：

[1] Nankai Univ, Dept Math, Tianjin 300071, Peoples R China

[2] Nankai Univ, LPMC, Tianjin 300071, Peoples R China

来源：

OPERATORS AND MATRICES | 2013年 / 7卷 / 01期

关键词：

Hilbert spaces; Banach spaces; Hilbert-Schauder frames; Hilbert-Schauder frame operators; ATOMIC DECOMPOSITIONS; BANACH-SPACES;

D O I：

10.7153/oam-07-04

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We introduce a new concept of frame operators for Banach spaces we call a Hilbert-Schauder frame operator. This is a hybird between standard frame theory for Hilbert spaces and Schauder frame theory for Banach spaces. Most of our results involve basic structure properties of the Hilbert-Schauder frame operator. Examples of Hilbert-Schauder frames include standard Hilbert frames and classical bases of l(p) and L-p-spaces with 1 < p <= 2. Finally, we give a new isomorphic characterization of Hilbert spaces.

引用

页码：91 / 99

页数：9

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