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This paper resolves a number of conjectures in the perturbation theory of linear operators. Namely, we prove that every Lipschitz function is operator Lipschitz in the Schatten-von Neumann ideals S α , 1 < α < ∞. The negative result for S α , α = 1, ∞ was earlier established by Yu. Farforovskaya in 1972. Alternatively, for every 1 < α < ∞, there is a… (More)

- D Potapov, F Sukochev
- 2008

The Haar system in the preduals of hyperfinite factors. Abstract We shall present examples of Schauder bases in the preduals to the hyperfinite factors of types II1, II∞, III λ , 0 < λ ≤ 1. In the semifinite (respectively, purely infinite) setting, these systems form Schauder bases in any associated separable symmetric space of measurable operators… (More)

We introduce a non-commutative Walsh system and prove that it forms a Schauder basis in the L p-spaces (1 < p < ∞) associated with the hyperfinite III λ-factors (0 < λ ≤ 1).

- I. A. Zhuravin, N. L. Tumanova, D. O. Potapov
- Journal of Evolutionary Biochemistry and…
- 2004

Suppose that f is a Lipschitz function on R with f Lip ≤ 1. Let A be a bounded self-adjoint operator on a Hilbert space H. Let p ∈ (1, ∞) and suppose that x ∈ B(H) is an operator such that the commutator [A, x] is contained in the Schatten class S p. It is proved by the last two authors, that then also [f (A), x] ∈ S p and there exists a constant C p… (More)

- I A Zhuravin, N L Tumanova, D O Potapov
- Zhurnal evoliutsionnoi biokhimii i fiziologii
- 2001

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