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Right and left quotient of two bounded operators on Hilbert spaces

Mohammed Benharrat
대한수학회 (The Korean Mathematical Society)|2020.04|대한수학회논문집 (Communications of the KMS)|제35권 제2호|pp. 547-563|DOI 10.4134/CKMS.c190111

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참고문헌

키워드

Moore-Penrose inverseBounded operators on Hilbert spacesright quotient of operatorsleft quotient of operators
주제분류수학

초록

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.

Abstract

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.

참고문헌 (22)

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