, Volume 9, Issue 2, pp 259-264

Subadditivity Inequalities in von Neumann Algebras and Characterization of Tracial Functionals

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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.

O.E. Tikhonov - Supported by the Russian Foundation for Basic Research (grant no. 01-01-00129) and the scientific program Universities of Russia – Basic Research (grant no. UR.04.01.061).