 

Ghadir Sadeghi and Reza Saadati
On geometrical properties of noncommutative modular function spaces view print


Published: 
August 15, 2015

Keywords: 
Measurable operator, von Neumann algebra, generalized singular value function, uniform Opial condition, KadecKlee property, modular function space. 
Subject: 
Primary 46L52. Secondary 46B20, 46A80. 


Abstract
We introduce and study the noncommutative modular function spaces of measurable operators affiliated with a semifinite von Neumann algebra and show that they are complete with respect to their modular. We prove that these spaces satisfy the uniform Opial condition with respect to
\widetilde{ρ}a.e.convergence for both the Luxemburg norm and the Amemiya norm. Moreover, these spaces have the uniform KadecKlee property
with respect to \widetilde{ρ}a.e.convergence when they are equipped with the Luxemburg norm. The above geometric properties
enable us to obtain some results in noncommutative Orlicz spaces.


Author information
Ghadir Sadeghi:
Department of Mathematics and Computer Sciences, Hakim Sabzevari University, P.O. Box 397, Sabzevar, IRAN
g.sadeghi@hsu.ac.ir
Reza Saadati:
Department of Mathematics, Iran University of Science and Technology, Tehran, Iran
rsaadati@eml.cc

