Linear transformations which preserve hermitian and positive semidefinite operators

John Emanuel de Pillis

Vol. 23 (1967), No. 1, 129–137

DOI: 10.2140/pjm.1967.23.129

Abstract

Let A and B represent the full algebras of linear operators on the finite-dimensional unitary spaces ℋ and 𝒦, respectively. The symbol ℒ(A,B) will denote the complex space of all linear maps from A to B. This paper concerns itself with the study of the following two cones in ℒ(A,B): (i) the cone 𝒞 of all T ∈ℒ(A,B) which send hermitian operators in A to hermitian operators in B, and (ii) the subcone 𝒞⁺ (of 𝒞) of all T ∈ℒ(A,B) which send positive semidefinite operators in A to positive semidefinite operators in B.

Mathematical Subject Classification

Primary: 15.40

Secondary: 47.00

Milestones

Received: 4 April 1966

Published: 1 October 1967