Means of Hilbert Space OperatorsSpringer Science & Business Media, 2002 - 134 pages |
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Algebraic arithmetic-geometric mean assume Ba(H Banach space bm e2x C1 H C₁(H Cetraro Chapter Choose and fix compute cosh cosh(x decomposition dominated convergence theorem double integral transformation dµ(x Editors equivalent estimate finite finite-rank operators fn(t Fourier transform geometric H₂ Heinz inequality Hence Hilbert space Hilbert space operators HX+XK implies integral expression kernel Kn)X L¹(R L¹(X L²(X L²(µ Lebesgue dominated convergence Lemma Let H M(Hn Ma(H matrix max{s mean inequality mean M(s monotone n=no norm inequalities Note obvious operator means operator norm operators H PnXPn positive operators proof of Theorem Remark satisfying Schur multiplier relative self-adjoint operators signed measure sinh sinh(gr strong convergence strong operator topology thanks Theorem 3.4 Theory trace class trace class operator unitarily invariant norm VIII weak operator topology XE B(H