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C*-algebra Positive Element Invertibility Criteria in Terms of L1-norms Equivalence and L∞-norms Equivalence

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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.

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Authors and Affiliations

  1. Lobachevskii Institute of Mathematics and Mechanics, Kazan (Volga region) Federal University, Kazan, 420008, Russia

    A. Novikov

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  1. A. Novikov
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Correspondence to A. Novikov.

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(Submitted by E. K. Lipachev)

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Novikov, A. C*-algebra Positive Element Invertibility Criteria in Terms of L1-norms Equivalence and L∞-norms Equivalence. Lobachevskii J Math 40, 677–680 (2019). https://doi.org/10.1134/S1995080219050159

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  • DOI: https://doi.org/10.1134/S1995080219050159

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