Gateaux derivative of matrix norms in operator spaces and operator systems

Abstract

We find expressions for the Gateaux derivative of the matrix norms in operator spaces, and operator systems. Some applications of the results to quantum probability measures, states on C${}^{\ast }$-algebras, and Birkhoff-James orthogonality are also presented.

arXiv commentSome errors from the previous version were corrected. To appear in J. Math. Anal. Appl