Fedor Anatol'evich Sukochev

THE KADEC-KLEE PROPERTY IN SYMMETRIC SPACES OF MEASURABLE OPERATORS

We show that ifE is a separable symmetric Banach function space on the positive half-line thenE has the Kadec-Klee property if and only if, for every semifinite von Neumann algebra (M, τ), the associated spaceE(M, τ) ofτ-measurable operators has the Kadec-Klee property.

Linear-topological classification of separableL p-spaces associated with von Neumann algebras of type I

AbstractWe classify, up to a linear-topological isomorphism, all separableLp-spaces, 1≤p<∞, associated with von Neumann algebras of type I. In particular, anyLp-space associated with an infinite-dimensional atomic von Neumann algebra is isomorphic tolp, or toCp, or to

Vilenkin systems and generalized triangular truncation operator

Sp = (\sum {_{n = 1}^\infty C_p^n )_{l_p } }

Lipschitz Continuity of the Absolute Value and Riesz Projections in Symmetric Operator Spaces

. Further, anyLp-space,p∈[1,∞),p∈2 associated with an infinite-dimensional von Neumann algebraM of type I is isomorphic to one of the following nine Banach spaces: lp, Lp, SP, Cp, Sp ⊕ Lp, Lp(Sp), Cp ⊕ Lp, Lp(Cp), Cp ⊕ Lp(Sp). In the casep=1 all the spaces in this list are pairwise non-isomorphic.

Differentiation of operator functions in non-commutative Lp-spaces

We prove a weak-type estimate for the absolute value mapping in the preduals of semifinite factors which extends an earlier result of Kosaki for the trace class.

Сравнение сумм независимых и дизъюнктных функций в симметричных пространствах@@@Comparison of Sums of Independent and Disjoint Functions in Symmetric Spaces

We study actions of the Vilenkin group ∏∞k=0ℤm(k) onLp-spaces associated with a semi-finite von Neumann algebra М, via a generalized triangular truncation operator. The systems of eigenspaces that arise contain the classical unbounded Vilenkin systems and we show that such systems with the inverse lexicographic enumeration form Schauder decompositions in all reflexive non-commutativeLp-spaces. This is a non-commutative analogue of a theorem of Paley for unbounded Vilenkin systems, which in the classical setting is due to W.S. Young, F. Schipp and P. Simon.