V. I. Chilin

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Articles: 5

Lie derivations on the algebras of locally measurable operators

Vladimir Chilin, Ilkhom Juraev

↓ Abstract   |   Article (.pdf)

MFAT 24 (2018), no. 1, 16-26


We prove that every Lie derivation on a solid $\ast$-subalgebra in an algebra of locally measurable operators is equal to a sum of an associative derivation and a center-valued trace.

Continuity of operator-valued functions in the $*$-algebra of locally measurable operators

V. I. Chilin, M. A. Muratov

↓ Abstract   |   Article (.pdf)

MFAT 20 (2014), no. 2, 124-133


In the present paper we establish sufficient conditions for a complex-valued function $f$ defined on $\mathbb{R}$ which guarantee continuity of an operator-function $T\mapsto f(T)$ w.r.t. the topology of local measure convergence in the $*$-algebra $LS(\mathcal{M})$ of all locally measurable operators affiliated to a von Neumann algebra $\mathcal{M}$.

Maharam traces on von Neumann algebras

V. I. Chilin, B. S. Zakirov

↓ Abstract   |   Article (.pdf)

MFAT 16 (2010), no. 2, 101-111


Traces $\Phi$ on von Neumann algebras with values in complex order complete vector lattices are considered. The full description of these traces is given for the case when $\Phi$ is the Maharam trace. The version of Radon-Nikodym-type theorem for Maharam traces is established.

Uniform equicontinuity for sequences of homomorphisms into the ring of measurable operators

V. I. Chilin, S. N. Litvinov

↓ Abstract   |   Article (.pdf)

MFAT 12 (2006), no. 2, 124-130


We introduce a notion of uniform equicontinuity for sequences of functions with the values in the space of measurable operators. Then we show that all the implications of the classical Banach Principle on the almost everywhere convergence of sequences of linear operators remain valid in a non-commutative setting.

On absract characterization of non-commutative $L_{p}$-spaces associated with center-valued trace

Vladimir I. Chilin, Alex Katz

MFAT 11 (2005), no. 4, 346-355


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