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This paper is concerned with perturbation formulae of the form∥f(a)−f(b)∥Lp(M,τ)⩽K∥a−b∥ Lp(M,τ) with K>0 being a constant depending on p and f only, where f is a real-valued Lipschitz function and a,b are self-adjoint τ-measurable operators affiliated with a semifinite von Neumann algebra (M,τ), such that the difference a−b belongs to L p (M,τ), 1<p<∞. In order to treat the situation...
We study the interplay between unconditional decompositions and the R-boundedness of collections of operators. In particular, we get several multiplier results of Marcinkiewicz type for $L^p$-spaces of functions with values in a Banach space X. Furthermore, we show connections between the above-mentioned properties and geometric properties of the Banach space X.
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