Vol. 23, No. 1, 1967

Download this article
Download this article. For screen
For printing
Recent Issues
Vol. 307: 1  2
Vol. 306: 1  2
Vol. 305: 1  2
Vol. 304: 1  2
Vol. 303: 1  2
Vol. 302: 1  2
Vol. 301: 1  2
Vol. 300: 1  2
Online Archive
The Journal
Editorial Board
Submission Guidelines
Submission Form
Policies for Authors
ISSN: 1945-5844 (e-only)
ISSN: 0030-8730 (print)
Special Issues
Author Index
To Appear
Other MSP Journals
Linear transformations which preserve hermitian and positive semidefinite operators

John Emanuel de Pillis

Vol. 23 (1967), No. 1, 129–137

Let A and B represent the full algebras of linear operators on the finite-dimensional unitary spaces and 𝒦, respectively. The symbol (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 (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
Received: 4 April 1966
Published: 1 October 1967
John Emanuel de Pillis