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

Abstract

We prove that the L₁-norms associated with a positive elements a^α is equivalent to the L₁-norm associated with a positive element a^β 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 a^α and a^β.