Publications (8)0.68 Total impact

Dataset: POSITIVITY2010

Dataset: POSITIVITY2010

Article: algebras and
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ABSTRACT: a certain class of operator  [Show abstract] [Hide abstract]
ABSTRACT: In the present paper we introduce a certain class of non commutative Orlicz spaces, associated with arbitrary faithful normal locallyfinite weights on a semifinite von Neumann algebra $M.$ We describe the dual spaces for such Orlicz spaces and, in the case of regular weights, we show that they can be realized as linear subspaces of the algebra of $LS(M)$ of locally measurable operators affiliated with $M.$08/2011; 53(4).  [Show abstract] [Hide abstract]
ABSTRACT: Given a von Neumann algebra $M$ with a faithful normal finite trace $\tau$ denote by $L^\Lambda(M, \tau)$ the generalized Arens algebra with respect to $M.$ We give a complete description of all additive derivations on the algebra $L^\Lambda(M, \tau).$ In particular each additive derivation on the algebra $L^{\Lambda}(M, \tau),$ where $M$ is a type II von Neumann algebra, is inner.Lobachevskii Journal of Mathematics 10/2010; 32(3). DOI:10.1134/S1995080211030024  [Show abstract] [Hide abstract]
ABSTRACT: In the present paper we introduce the notion of Arens space associated with a finite von Neumann algebra and a faithful normal finite state. Relations between these spaces and Arens algebras with respect to traces are investigated. Keywordsvon Neumann algebraTraceStateArens algebraArens space Mathematics Subject Classification (2000)46L5146L5246L07Positivity 03/2010; 14(1):105121. DOI:10.1007/s1111700900085 · 0.68 Impact Factor  [Show abstract] [Hide abstract]
ABSTRACT: Given a von Neumann algebra $M$ with a faithful normal finite trace, we introduce the so called finite tracial algebra $M_f$ as the intersection of $L_p$spaces $L_p(M, \mu)$ over all $p \geq 1$ and over all faithful normal finite traces $\mu$ on $M.$ Basic algebraic and topological properties of finite tracial algebras are studied. We prove that all derivations on these algebras are inner.  [Show abstract] [Hide abstract]
ABSTRACT: no. 419 Diese Arbeit ist mit Unterstützung des von der Deutschen Forschungsgemeinschaft getragenen Sonderforschungsbereichs 611 an der Universität Bonn entstanden und als Manuskript vervielfältigt worden. Abstract Given a von Neumann algebra M with a faithful normal finite trace, we introduce the so called finite tracial algebra M f as the intersection of L p spaces L p (M, µ) over all p ≥ 1 and all faithful normal finite traces µ on M. Basic algebraic and topological properties of these algebras are studied.
Publication Stats
15  Citations  
0.68  Total Impact Points  
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Institutions

2011

Tashkent State Agrarian University
Toshkent, Toshkent Shahri, Uzbekistan


2009–2010

Uzbekistan Academy of Sciences
Toshkent, Toshkent Shahri, Uzbekistan
