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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