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Joint Convexity and Concavity of N-tuples τ-Measurable Positive Operator Trace Functions

Author: MaiHeMuTi·MaiMaiTi
Tutor: TuErDeBieKe
School: Xinjiang University
Course: Basic mathematics
Keywords: Semi-finite von Neumann algebras Jointly convex Jointly concave Operator concave Operator convex
CLC: O177
Type: Master's thesis
Year: 2011
Downloads: 2
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Abstract


In this thesis, we consider the noncommutative Lp(M;τ) spaces associated with asemifinite von Neumann algebra M.Firstly, We give the prove that n- tuplesτ-measurable trace functionF(x,y) =τ(xp +yp1/pis jointly convex and jointly concave in (x,y). Secondly, We obtain the necessary andsuffcient condition of theτ-measurable trace functionis jointly convex and jointly concave in (x1,x2,···,xn).

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CLC: > Mathematical sciences and chemical > Mathematics > Mathematical Analysis > Functional Analysis
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