Description of the Real von Neumann Algebras with Abelian Skew-Symmetric Part

In this note we describe (up to isomorphism) the real von Neiman algebras R with Abelian skew-symmetric part , i.e., such that xy-yx=0 for any .     

Real <Emphasis Type="Italic">AW</Emphasis><Superscript>*</Superscript>-Algebras of type I

Let R be a real AW ^*-algebra, and suppose that its complexification M = R + iR is also a (complex) AW ^*-algebra. We prove that R is of type I if and only if so is M.Translated from Funktsionalnyi Analiz i Ego Prilozheniya, Vol. 38, No. 4, pp. 79–81, 2004Original Russian Text Copyright © by Sh. A. Ayupov     

Spatiality of Derivations on the Algebra of τ-Compact Operators

This paper is devoted to derivations on the algebra S ₀(M, τ) of all τ-compact operators affiliated with a von Neumann algebra M and a faithful normal semi-finite trace τ. The main result asserts that every t _τ -continuous derivation ${D : S_0(M, \tau) \rightarrow S_{0}(M, \tau)}$ is spatial and implemented by a τ-measurable operator affiliated with M, where t _τ denotes the measure topology on S ₀(M, τ). We also show the automatic t _τ -continuity of all derivations on S ₀(M, τ) for properly infinite von Neumann algebras M. Thus in the properly infinite case the condition of t _τ -continuity of the derivation is redundant for its spatiality.     

Local and 2-local derivations on noncommutative Arens algebras

The paper is devoted to so-called local and 2-local derivations on the noncommutative Arens algebra L ^ω(M,τ) associated with a von Neumann algebra M and a faithful normal semi-finite trace τ. We prove that every 2-local derivation on L ^ω(M,τ) is a spatial derivation, and if M is a finite von Neumann algebra, then each local derivation on L ^ω(M,τ) is also a spatial derivation and every 2-local derivation on M is in fact an inner derivation.     

Jordan operator algebras

A survey of recent results in classification of JW-algebras (weakly closed Jordan algebras of self-adjoint operators in the Hilbert space) is given along with connections of JW-algebras with their enveloping W^*-algebras. It is shown how these results are applied in the proofs of analogs of many important results in the theory of W^*-algebras.Translated from Itogi Nauki i Tekhniki, Seriya Sovremennye Problemy Matematiki (Noveishie Dostizheniya), Vol. 27, pp. 67–98, 1985.     

Optical characteristics of thin rutile films on fused quartz substrates

Polycrystalline rutile films are synthesized on fused quartz substrates by the method of thermal oxidation of a titanium metal layer in air at 800°C. The optical parameters of the TiO ₂ films are determined for a wavelength of λ = 0.6328 μm by the method of laser zero ellipsometry. __________ Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 5, pp. 15–20, May, 2006.     

Synthesis of Nitro,Amino, and Halo Derivatives of 2-Ethyl-2-methyl-2,3-dihydro-1H-indole

Russian Journal of Organic Chemistry - The nitration, oxidative halogenation, and radical bromination and chlorination of 2-ethyl-2-methyl-2,3-dihydro-1H-indole afforded the corresponding nitro,...