Positive solutions to the equations AX = C and XB = D for Hilbert space operators

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:333

Article

Dajic, Alegra ; Koliha, J. J.

关键词: Hilbert space;    operator equation;    positive solution;    common positive solutions;   

DOI  :  10.1016/j.jmaa.2006.11.016

来源: Elsevier

【 摘 要 】

The paper studies the equation AX = C for bounded linear operators between Hilbert spaces, gives conditions for the existence of hermitian solutions and positive solutions, and obtains the formula for the general form of these solutions. Then the common hermitian and positive solutions to the equations A X = C and X,9 = D are studied and new representations of the general solutions are given. Many results for matrices are recovered as special cases, and the results of Phadke and Thakare [S.V. Phadke, N.K. Thakare, Generalized inverses and operator equations, Linear Algebra Appl. 23 (1979) 191-199] are corrected. (c) 2006 Elsevier Inc. All rights reserved.

【 授权许可】

Free