Hilbert空间上连续算子值框架的不相交性

J4 ›› 2011, Vol. 46 ›› Issue (4): 103-107.

Hilbert空间上连续算子值框架的不相交性

李丹，孟彬

南京航空航天大学理学院，江苏南京 210016

收稿日期:2010-05-21 发布日期:2011-04-21
作者简介:李丹(1986- ),女,硕士研究生, 研究方向为算子与小波. Email: lidan6956@163.com
基金资助:
南京航空航天大学基本科研业务费专项资金资助(NS20100197)

Disjointness for continuous operator-valued frames in Hilbert spaces

LI Dan, MENG Bin

Department of Mathematics, Nanjing University of Aeronautics and Astronautics, Nanjing 210016, Jiangsu China

Received:2010-05-21 Published:2011-04-21

摘要/Abstract

摘要：

引入Hilbert 空间连续算子值框架的不相交性、强不相交性、强补框架的定义, 讨论它们的性质;引入保不相交算子、强保不相交算子, 证明了酉算子可逆算子是强保不相交算子, 下有界算子余等距算子是保不相交算子。

关键词: 连续算子值框架; 不相交性; 保不相交算子

Abstract:

The paper introduces the definitions of continuous operator-valued frame disjointness, strong disjointness strong complement and discusses their properties in Hilbert spaces. Then disjointness-preseving operators, strong disjointness-preseving operators are introduced. It proves that unitary operators,invertible operators are strong disjointness-preseving operators and lower bounded operators, isometric operators are disjointness-preseving operators.

Key words: continuous operator-valued frames; disjointness; disjointness-preseving operator

李丹，孟彬. Hilbert空间上连续算子值框架的不相交性[J]. J4, 2011, 46(4): 103-107.

LI Dan, MENG Bin. Disjointness for continuous operator-valued frames in Hilbert spaces[J]. J4, 2011, 46(4): 103-107.

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