Hilbert C*-模H中的伪框架分解

数学季刊 ›› 2010, Vol. 25 ›› Issue (2): 276-281.

Hilbert C*-模H中的伪框架分解

Department of Mathematics, Yuncheng University

收稿日期:2005-10-27 出版日期:2010-06-30 发布日期:2023-06-05
作者简介: YAO Xi-yan(1963-), female, native of Wenxi, Shanxi, a professor of Yungcheng University, Ph.D., engages in wavelet analysis.
基金资助:
Supported by the Emphasis Supported Subject Foundation of Shanxi Province(20055026)； Supported by the Emphasis Science Foundation of Yuncheng University(20060103)；

Pseudo Frame Decompositions in a Hilbert C^∗-module H

Department of Mathematics, Yuncheng University

Received:2005-10-27 Online:2010-06-30 Published:2023-06-05
About author: YAO Xi-yan(1963-), female, native of Wenxi, Shanxi, a professor of Yungcheng University, Ph.D., engages in wavelet analysis.
Supported by:
Supported by the Emphasis Supported Subject Foundation of Shanxi Province(20055026)； Supported by the Emphasis Science Foundation of Yuncheng University(20060103)；

摘要/Abstract

摘要： In the paper, we introduce weak Bessel sequences and weak frames in a Hilbert C*-module H, and give a characterization of weak Bessel sequences, weak frames, normalized tight weak frames, and dual weak frames to each other, respectively. Using A-valued linear bounded operator U:H → l²(A), V*U = I, a coustructing method of dual weak frame {x*_j: j ∈ J} for a given weak frame {x_j: j ∈ J} is obtained. Moreover, pseudo frame decompositions for H is given.

关键词: C*-algebra, Hilbert C*-module frame, dual frame, frame decomposition

Abstract: In the paper, we introduce weak Bessel sequences and weak frames in a Hilbert C*-module H, and give a characterization of weak Bessel sequences, weak frames, normalized tight weak frames, and dual weak frames to each other, respectively. Using A-valued linear bounded operator U:H → l²(A), V*U = I, a coustructing method of dual weak frame {x*_j: j ∈ J} for a given weak frame {x_j: j ∈ J} is obtained. Moreover, pseudo frame decompositions for H is given.

Key words: C*-algebra, Hilbert C*-module frame, dual frame, frame decomposition

中图分类号:

O177.1

姚喜妍. Hilbert C*-模H中的伪框架分解[J]. 数学季刊, 2010, 25(2): 276-281.

YAO Xi-yan. Pseudo Frame Decompositions in a Hilbert C^∗-module H [J]. Chinese Quarterly Journal of Mathematics, 2010, 25(2): 276-281.

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