Dilation of Dual Frame Pairs in Hilbert C*-Modules

被引：17

作者：

Han, Deguang ^{[1
]}

Jing, Wu ^{[2
]}

Larson, David ^{[3
]}

Li, Pengtong ^{[4
]}

Mohapatra, Ram N. ^{[1
]}

机构：

[1] Univ Cent Florida, Dept Math, Orlando, FL 32816 USA

[2] Fayetteville State Univ, Dept Math & Comp Sci, Fayetteville, NC 28301 USA

[3] Texas A&M Univ, Dept Math, College Stn, TX 77843 USA

[4] Nanjing Univ Aeronaut & Astronaut, Dept Math, Nanjing 210016, Jiangsu, Peoples R China

来源：

RESULTS IN MATHEMATICS | 2013年 / 63卷 / 1-2期

关键词：

Frames; Riesz bases; dilation; dual frame pairs; frame vectors; unitary groups; Hilbert C*-modules; ALGEBRAS;

D O I：

10.1007/s00025-011-0195-9

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We investigate the geometric properties for Hilbert C*-modular frames. We show that any dual frame pair in a Hilbert C*-module is an orthogonal compression of a Riesz basis and its canonical dual for some larger Hilbert C*-module. This generalizes the Hilbert space dual frame pair dilation theory due to Casazza, Han and Larson to dual Hilbert C*-modular frame pairs. Additionally, for any Hilbert C*-modular dual frame pair induced by a group of unitary operators, we show that there is a dilated dual pair which inherits the same group structure.

引用

页码：241 / 250

页数：10

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