Positivity

, Volume 9, Issue 2, pp 259–264 | Cite as

Subadditivity Inequalities in von Neumann Algebras and Characterization of Tracial Functionals

Article

Abstract

We examine under which assumptions on a positive normal functional φ on a von Neumann algebra, \({\cal M}\) and a Borel measurable function f: R+R with f(0) = 0 the subadditivity inequality φ (f(A+B)) ≤ φ(f(A))+φ (f (B)) holds true for all positive operators A, B in \({\cal M}\). A corresponding characterization of tracial functionals among positive normal functionals on a von Neumann algebra is presented.

Keywords

algebra of matrices functional calculus positive normal functional subadditivity inequality tracial functional von Neumann algebra 

2000 Mathematics Subject classification

46L30 15A45 

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Copyright information

© Springer 2005

Authors and Affiliations

  1. 1.Research Institute of Mathematics and MechanicsKazan State UniversityKazanRussia

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