C*-algebra Positive Element Invertibility Criteria in Terms of L1-norms Equivalence and L∞-norms Equivalence
- Authors: Novikov A.1
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Affiliations:
- Lobachevskii Institute of Mathematics and Mechanics
- Issue: Vol 40, No 5 (2019)
- Pages: 677-680
- Section: Article
- URL: https://journals.rcsi.science/1995-0802/article/view/204513
- DOI: https://doi.org/10.1134/S1995080219050159
- ID: 204513
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Abstract
We prove that the L1-norms associated with a positive elements aα is equivalent to the L1-norm associated with a positive element aβ if and only if it is equivalent to the natural norm of a C*-algebra, which means the invertibility of a in the case of unital C*-algebra. The same propositions are proved for L∞-norms associated with positive element aα and aβ.
About the authors
A. Novikov
Lobachevskii Institute of Mathematics and Mechanics
Author for correspondence.
Email: a.hobukob@gmail.com
Russian Federation, Kazan, 420008