Title: Linear transformations which preserve trace and positive semidefiniteness of operators
Abstract: This work may be considered a completion of the paper by J. de Pillis: Linear transformations which preserve Hermitian and positive semidefinite operators, published in 1967 [2]: necessary conditions have been formulated. Let A1 be the full algebra of linear operators on the n-dimensional Hilbert space H1, and let A2 be the full algebra of linear operators on the m-dimensional Hilbert space H2. Let L(A1,A2) denote the complex spaceof linear maps from A1 to A2 and S denotes the cone of all T ϵ L(A1,A2 which send positive semidefinite operators from A1 to positive semidefinite operators from A2. The aim of this paper is to present a necessary and sufficient condition for a transformation in L(A1, A2) to be in the cone S, and to preserve trace of the operators.
Publication Year: 1972
Publication Date: 1972-12-01
Language: en
Type: article
Indexed In: ['crossref']
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Cited By Count: 1273
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