Title : ( Halmos' two projections theorem for Hilbert C⁎-module operators and the Friedrichs angle of two closed submodules )
Authors: Wei Luo , Mohammad Sal Moslehian , Qingxiang Xu ,
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Abstract
Halmos’ two projections theorem for Hilbert space operators is one of the fundamental results in operator theory. In this paper, we introduce the term of two harmonious projections in the context of adjointable operators on Hilbert C∗-modules, extend Halmos’ two projections theorem to the case of two harmonious projections. We also give some new characteri-zations of the closed submodules and their associated pro-jections. As an application, a norm equation associated to a characterization of the Friedrichs angle is proved to be true in the framework of Hilbert C∗-modules.
Keywords
, Hilbert C∗, module Orthogonal complement Halmos’ two projections theorem Friedrichs angle
@article{paperid:1074155,
author = {Wei Luo and Sal Moslehian, Mohammad and Qingxiang Xu},
title = {Halmos' two projections theorem for Hilbert C⁎-module operators and the Friedrichs angle of two closed submodules},
journal = {Linear Algebra and its Applications},
year = {2019},
volume = {577},
month = {September},
issn = {0024-3795},
pages = {134--158},
numpages = {24},
keywords = {Hilbert C∗-module
Orthogonal complement
Halmos’ two projections theorem
Friedrichs angle},
}
%0 Journal Article
%T Halmos' two projections theorem for Hilbert C⁎-module operators and the Friedrichs angle of two closed submodules
%A Wei Luo
%A Sal Moslehian, Mohammad
%A Qingxiang Xu
%J Linear Algebra and its Applications
%@ 0024-3795
%D 2019
