Journal
POSITIVITY
Volume 9, Issue 2, Pages 259-264Publisher
SPRINGER
DOI: 10.1007/s11117-005-2711-1
Keywords
algebra of matrices; functional calculus; positive normal functional; subadditivity inequality; tracial functional; von Neumann algebra
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We examine under which assumptions on a positive normal functional phi on a von Neumann algebra, M and a Borel measurable function f: R+ -> R with f(0) = 0 the subadditivity inequality phi(f(A+B)) <= phi(f(A)) +phi(f (B)) holds true for all positive operators A, B in M. A corresponding characterization of tracial functionals among positive normal functionals on a von Neumann algebra is presented.
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