Rearrangements of Tripotents and Differences of Isometries in Semifinite von Neumann Algebras
- Authors: Bikchentaev A.M.1
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Affiliations:
- N. I. Lobachevskii Institute of Mathematics and Mechanics
- Issue: Vol 40, No 10 (2019)
- Pages: 1450-1454
- Section: Article
- URL: https://journals.rcsi.science/1995-0802/article/view/205635
- DOI: https://doi.org/10.1134/S1995080219100068
- ID: 205635
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Abstract
Let τ be a faithful normal semifinite trace on a von Neumann algebra ℳ, and ℳu be a unitary part of ℳ. We prove a new property of rearrangements of some tripotents in ℳ. If V ∈ ℳ is an isometry (or a coisometry) and U − V is τ-compact for some U ∈ ℳu then V ∈ ℳu. Let ℳ be a factor with a faithful normal trace τ on it. If V ∈ ℳ is an isometry (or a coisometry) and U − V is compact relative to ℳ for some U ∈ ℳu then V ∈ ℳu. We also obtain some corollaries.
About the authors
A. M. Bikchentaev
N. I. Lobachevskii Institute of Mathematics and Mechanics
Author for correspondence.
Email: Airat.Bikchentaev@kpfu.ru
Russian Federation, Kazan, Tatarstan, 420008