Published in Journal of Physics A: Mathematical and Theoretical
We introduce quantum monadic and quantum cylindric algebras. These are adaptations to the quantum setting of the monadic algebras of Halmos, and cylindric algebras of Henkin, Monk and Tarski, that are used in algebraic treatments of classical and intuitionistic predicate logic. Primary examples in the quantum setting come from von Neumann algebras ...
Published in Journal of Physics A: Mathematical and Theoretical
The rather unintuitive nature of quantum theory has led numerous people to develop sets of (physically motivated) principles that can be used to derive quantum mechanics from the ground up, in order to better understand where the structure of quantum systems comes from. From a computer scientist’s perspective we would like to study quantum theory i...
Published in Lobachevskii Journal of Mathematics
AbstractThe present paper is devoted to study of ring isomorphisms of \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\ast$$\end{document}-subalgebras of Murray–von Neu...
Published in Lobachevskii Journal of Mathematics
AbstractIt is proved that the inequality\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\varphi(A)\leq\varphi(|A+\textrm{i}B|)\quad\text{for all}\quad A\in\mathcal{A}^{...
Published in Lobachevskii Journal of Mathematics
AbstractWe consider a tracial state \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\varphi$$\end{document} on a von Neumann algebra \documentclass[12pt]{minimal} \usep...
Let be a von Neumann algebra without nonzero central abelian projections on a complex Hilbert space . Let pn (X 1 , X 2 , · · ·, Xn ) be the polynomial defined by n indeterminates X 1, · · ·, Xn and their Jordan multiple ∗-products. In this paper it is shown that a family 𝒟 = {dm } m ∈ℕ of mappings such that , the identity map on satisfies the c...
status: published
Published in Russian Mathematics
Let τ be a faithful normal semifinite trace on a von Neumann algebra. We establish the Leibniz criterion for sign-alternating series of τ-measurable operators and present an analogue of the criterion of series “sandwich” series for τ-measurable operators. We prove a refinement of this criterion for the τ-compact case. In terms of measure convergenc...
Published in Complex Analysis and Operator Theory
Let A be a closed subalgebra of a C∗\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$C^*$$\end{document}-algebra, that is a norm-closed algebra of Hilbert space operator...
Published in Mathematical Notes
Let ϕ be a subadditive weight on a C* -algebra A, and let Mϕ+ be the set of all elements x in A+ with ϕ(x)
