Klyachko’s Theorem in Semi-finite von Neumann Algebras

Abstract

Let A be a von Neumann algebra and A be the set of all τ-measurable operators. For positive elements A and B in A we prove that

∫_K_ µs (A + B) ds ≤ ∫_K_ µs (A) ds + ∫_K_ µs (B) ds,

where µ(·) denotes the generalized s-number and I, J, and K are on an analogue of the Klyachko list.