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Paper's Title:
On Closed Range C*-modular Operators
Author(s):
Javad Farokhi-Ostad and Ali Reza Janfada
Department of Mathematics,
Faculty of Mathematics and Statistics Sciences,
University of Birjand, Birjand,
Iran.
E-mail: j.farokhi@birjand.ac.ir
ajanfada@birjand.ac.ir
Abstract:
In this paper, for the class of the modular operators on Hilbert C*-modules, we give the conditions to closedness of their ranges. Also, the equivalence conditions for the closedness of the range of the modular projections on Hilbert C*-modules are discussed. Moreover, the mixed reverse order law for the Moore-Penrose invertible modular operators are given.
Paper's Title:
On Commutator of Aluthge Transforms and Fuglede-Putnam Property
Author(s):
(Manzar Maleki, Ali Reza Janfada and Seyed Mohammad Sadegh Nabavi Sales
International Campus, Faculty of
Mathematical Sciences,
Ferdowsi University of Mashhad, Mashhad,
Iran.
E-mail: manzar.maleki@gmail.com
Faculty of Mathematics and Statistics,
Department of Mathematics,
University of Birjand,
P. O. Box 414, Birjand 9717851367,
Iran.
E-mail: ajanfada@birjand.ac.ir
Department of Pure Mathematics, Hakim
Sabzevari University,
P.O. Box 397, Sabzevar,
Iran.
E-mail: sadegh.nabavi@hsu.ac.ir
Abstract:
We deal with the well-known Fuglede-Putnam theorem and related FP-property. We show that if
(A,B) has the FP-property, then so has
where 0≤
t1,t2≤1 are arbitrary.
We first prove that
if and only if
AX=XB for all X, whenever (A,B) has the FP-property. We
prove some similar results for
instead of $
as well. Also we introduce the sequence of generalized iterations of Aluthge transform of operators and express some results for this notion associated to the FP-property.
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