On Pták functions for bounded operators

  • Abdellah El Kinani
Keywords: Pseudo-Hilbertizable space, Hilbert space, Normed algebra, Q-algebra, Hermitian element, Hermitian Banach algebra, Pták function, Bounded linear operator, C*-algebra, Mobius transformation

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.
Published
2014-10-13
Section
Articoli