, Volume 9, Issue 2, pp 259–264

Subadditivity Inequalities in von Neumann Algebras and Characterization of Tracial Functionals


DOI: 10.1007/s11117-005-2711-1

Cite this article as:
Tikhonov, O.E. Positivity (2005) 9: 259. doi:10.1007/s11117-005-2711-1


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.


algebra of matricesfunctional calculuspositive normal functionalsubadditivity inequalitytracial functionalvon Neumann algebra

2000 Mathematics Subject classification


Copyright information

© Springer 2005

Authors and Affiliations

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