Differences of idempotents in C*-algebras
- Authors: Bikchentaev A.M.1
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Affiliations:
- Kazan Federal University
- Issue: Vol 58, No 2 (2017)
- Pages: 183-189
- Section: Article
- URL: https://journals.rcsi.science/0037-4466/article/view/171046
- DOI: https://doi.org/10.1134/S003744661702001X
- ID: 171046
Cite item
Abstract
Suppose that P and Q are idempotents on a Hilbert space H, while Q = Q* and I is the identity operator in H. If U = P − Q is an isometry then U = U* is unitary and Q = I − P. We establish a double inequality for the infimum and the supremum of P and Q in H and P − Q. Applications of this inequality are obtained to the characterization of a trace and ideal F-pseudonorms on a W*-algebra. Let φ be a trace on the unital C*-algebra A and let tripotents P and Q belong to A. If P − Q belongs to the domain of definition of φ then φ(P − Q) is a real number. The commutativity of some operators is established.
About the authors
A. M. Bikchentaev
Kazan Federal University
Author for correspondence.
Email: Airat.Bikchentaev@kpfu.ru
Russian Federation, Kazan