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How and Why to Solve the Operator Equation AX − XB = Y
Author(s) -
Bhatia Rajendra,
Rosenthal Peter
Publication year - 1997
Publication title -
bulletin of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 2.396
H-Index - 48
eISSN - 1469-2120
pISSN - 0024-6093
DOI - 10.1112/s0024609396001828
Subject(s) - mathematics , linear operators , bounded function , banach space , mathematics subject classification , linear map , bounded operator , operator (biology) , pure mathematics , space (punctuation) , vector space , finite rank operator , continuous linear operator , discrete mathematics , algebra over a field , mathematical analysis , biochemistry , chemistry , repressor , transcription factor , gene , linguistics , philosophy
The entities A, B, X, Y in the title are operators , by which we mean either linear transformations on a finite‐dimensional vector space (matrices) or bounded (= continuous) linear transformations on a Banach space. (All scalars will be complex numbers.) The definitions and statements below are valid in both the finite‐dimensional and the infinite‐dimensional cases, unless the contrary is stated. 1991 Mathematics Subject Classification 15A24, 47A10, 47A62, 47B47, 47B49, 65F15, 65F30.