C*-algebra positive element invertibility criteria in terms of $L_1$-norms equivalence

Abstract

We prove that the $L_1$-norms associated with a positive element $a$ of a unital C*-algebra are equivalent to the norm of C*-algebra if and only if $a$ is invertible.

References in corpus (2)

• Characterization of central elements of operator algebras by inequalities
• $L_1$-space for a positive operator affiliated with von Neumann algebra