Title : ( Douglas range factorization theorem for regular operators on Hilbert C∗-modules )
Authors: Marzieh Forough , Asadollah Niknam ,
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Abstract
In this paper, we aim to extend the Douglas range factorization theorem from the context of Hilbert spaces to the context of regular operators on a Hilbert C∗-module. In particular, we show that if t and s are regular operators on a Hilbert C∗-module E such that ran (t) ⊆ ran (s) and if s has a generalized inverse s†, then r = s†t is a densely defined operator satisfying t = sr. Moreover, if s is boundedly adjointable, then r is closed densely defined and its graph is orthogonally complemented in E ⊕ E, and if t is boundedly adjointable, then r is boundedly adjointable.
Keywords
, Hilbert C∗-modules, regular operators, range factorization.
@article{paperid:1037259,
author = {Forough, Marzieh and Niknam, Asadollah},
title = {Douglas range factorization theorem for regular operators on Hilbert C∗-modules},
journal = {Rocky Mountain Journal of Mathematics},
year = {2013},
volume = {43},
number = {5},
month = {January},
issn = {0035-7596},
pages = {1513--1520},
numpages = {7},
keywords = {Hilbert C∗-modules; regular operators; range factorization.},
}
%0 Journal Article
%T Douglas range factorization theorem for regular operators on Hilbert C∗-modules
%A Forough, Marzieh
%A Niknam, Asadollah
%J Rocky Mountain Journal of Mathematics
%@ 0035-7596
%D 2013
