On Pták functions for bounded operators

Abstract

The purpose of this paper is to prove that if the Pták function p is an operator norm, on \mathcal{B}(E), associated to a norm | . |, then (E, | . |) is a pseudo-Hilbert space. As a consequence, we obtain that if \mathcal{B}(E) is a C*-algebra, then E is a Hilbert space.

Keywords

• Pseudo-Hilbertizable space
• Hilbert space
• Normed algebra
• Q-algebra
• Hermitian element
• Hermitian Banach algebra
• Pták function
• Bounded linear operator
• C*-algebra
• Mobius transformation