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We define a left quotient as well as a right quotient of two bounded operators between Hilbert spaces, and we parametrize these two concepts using the Moore-Penrose inverse. In particular, we show that the adjoint of a left quotient is a right quotient and conversely. An explicit formulae for computing left (resp.~right) quotient which correspond to adjoint, sum, and product of given left (resp.~right) quotient of two bounded operators are also shown.
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참고문헌 (22)
참고문헌 신청
M. Benharrat / 2013 / Semi-Fredholm operators and pure contractions in Hilbert space / Rend. Circ. Mat. Palermo (2) 62(2):267~272
M. Benharrat / 2015 / Strong metrizability for closed operators and the semi-Fredholm operators between two Hilbert spaces / Int. J. Anal. Appl 8(2):110~122
A. Ben-Israel / 2003 / Generalized inverses: theory and applications / Springer
R. G. Douglas / 1966 / On majorization, factorization, and range inclusion of operators on Hilbert space / Proc. Amer. Math. Soc 17:413~415
J. Dixmier / 1949 / Etude sur les vari´et´es et les op´erateurs de Julia, avec quelques applications ´ / Bull. Soc. Math. France 77:11~101
M. Benharrat / 2015 / Strong metrizability for closed operators and the semi-Fredholm operators between two Hilbert spaces / Int. J. Anal. Appl 8(2):110~122
A. Ben-Israel / 2003 / Generalized inverses: theory and applications / Springer
R. G. Douglas / 1966 / On majorization, factorization, and range inclusion of operators on Hilbert space / Proc. Amer. Math. Soc 17:413~415
J. Dixmier / 1949 / Etude sur les vari´et´es et les op´erateurs de Julia, avec quelques applications ´ / Bull. Soc. Math. France 77:11~101
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