Title : ( Moore-Penrose inverses of Gram operators on Hilbert C*-modules )
Authors: Mohammad Sal Moslehian , Kamran Sharifi , Marzieh Forough , Mahnaz Chakoshi ,
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Abstract
Let $t$ be a regular operator between Hilbert $C^*$-modules and $t^\\\\dag$ be its Moore-Penrose inverse. We investigate the Moore-Penrose invertibility of the Gram operator $t^*t$. More precisely, we study some conditions ensuring that $t^{ \\\\dag} = (t^* \\\\, t)^{ \\\\dag} \\\\, t^*= t^*\\\\,(t \\\\, t^*)^{ \\\\dag}$ and $(t^*t)^{ \\\\dag}=t^{ \\\\dag}t^{* \\\\, \\\\dag}$ hold. As an application, we get some results for densely defined closed operators on Hilbert $C^*$-modules over $C^*$-algebras of compact operators.
Keywords
, Unbounded operator, Moore-Penrose inverse, Hilbert $C^*$-module, $C^*$-algebra, $C^*$-algebra of compact operators
@article{paperid:1029099,
author = {Sal Moslehian, Mohammad and Kamran Sharifi and Forough, Marzieh and Mahnaz Chakoshi},
title = {Moore-Penrose inverses of Gram operators on Hilbert C*-modules},
journal = {Studia Mathematica},
year = {2012},
volume = {210},
number = {2},
month = {December},
issn = {0039-3223},
pages = {189--196},
numpages = {7},
keywords = {Unbounded operator; Moore-Penrose inverse; Hilbert
$C^*$-module; $C^*$-algebra; $C^*$-algebra of compact operators},
}
%0 Journal Article
%T Moore-Penrose inverses of Gram operators on Hilbert C*-modules
%A Sal Moslehian, Mohammad
%A Kamran Sharifi
%A Forough, Marzieh
%A Mahnaz Chakoshi
%J Studia Mathematica
%@ 0039-3223
%D 2012
