New York Journal of Mathematics
Volume 21 (2015) 759-781


Ghadir Sadeghi and Reza Saadati

On geometrical properties of noncommutative modular function spaces

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Published: August 15, 2015
Keywords: Measurable operator, von Neumann algebra, generalized singular value function, uniform Opial condition, Kadec-Klee property, modular function space.
Subject: Primary 46L52. Secondary 46B20, 46A80.

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 Kadec-Klee 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

Reza Saadati:
Department of Mathematics, Iran University of Science and Technology, Tehran, Iran