


Paper's Title:
On Closed Range C^{*}modular Operators
Author(s):
Javad FarokhiOstad and Ali Reza Janfada
Department of Mathematics,
Faculty of Mathematics and Statistics Sciences,
University of Birjand, Birjand,
Iran.
Email: 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 MoorePenrose invertible modular operators are given.
Paper's Title:
On Commutator of Aluthge Transforms and FugledePutnam 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.
Email: manzar.maleki@gmail.com
Faculty of Mathematics and Statistics,
Department of Mathematics,
University of Birjand,
P. O. Box 414, Birjand 9717851367,
Iran.
Email: ajanfada@birjand.ac.ir
Department of Pure Mathematics, Hakim
Sabzevari University,
P.O. Box 397, Sabzevar,
Iran.
Email: sadegh.nabavi@hsu.ac.ir
Abstract:
We deal with the wellknown FugledePutnam theorem and related FPproperty. We show that if (A,B) has the FPproperty, then so has where 0≤ t_{1},t_{2}≤1 are arbitrary. We first prove that if and only if AX=XB for all X, whenever (A,B) has the FPproperty. 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 FPproperty.
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