Recent zbMATH articles in MSC 17Chttps://zbmath.org/atom/cc/17C2021-07-26T21:45:41.944397ZWerkzeugReversible AJW-algebrashttps://zbmath.org/1463.460962021-07-26T21:45:41.944397Z"Ayupov, Shavkat Abdullaevich"https://zbmath.org/authors/?q=ai:ayupov.sh-a"Arzikulov, Farhodjon Nematjonovich"https://zbmath.org/authors/?q=ai:arzikulov.farhodjon-nematjonovichSummary: The main result states that every special AJW-algebra can be decomposed into the direct sum of totally irreversible and reversible subalgebras. In turn, every reversible special AJW-algebra decomposes into a direct sum of two subalgebras, one of which has purely real enveloping real von Neumann algebra, and the second one contains an ideal, whose complexification is a \(C^*\)-algebra and the annihilator of this complexification in the enveloping \(C^*\)-algebra of this subalgebra is equal to zero.On the uniform zero-two law for positive contractions of Jordan algebrashttps://zbmath.org/1463.470402021-07-26T21:45:41.944397Z"Mukhamedov, Farrukh"https://zbmath.org/authors/?q=ai:mukhamedov.farruh-mSummary: Following an idea of \textit{D. Ornstein} and \textit{L. Sucheston} [Ann. Math. Stat. 41, 1631--1639 (1970; Zbl 0284.60068)], \textit{S. R. Foguel} [Isr. J. Math. 10, 275--280 (1971; Zbl 0229.60056)] proved the so-called uniform ``zero-two'' law: let \(T: L^1(X,\mathcal{F}, \mu)\to L^1(X,\mathcal{F}, \mu)\) be a positive contraction. If for some \(m\in\mathbb{N}\cup\{0\}\) one has \(||T^{m+1}-T^m||<2\), then \[\lim_{n\to\infty}|| T^{m+1}-T^m||=0.\]
In this paper we prove a non-associative version of the unform ``zero-two'' law for positive contractions of \(L_1\)-spaces associated with \(JBW\)-algebras.