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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

Quotients of bounded operators


Author: Saichi Izumino
Journal: Proc. Amer. Math. Soc. 106 (1989), 427-435
MSC: Primary 47A05
DOI: https://doi.org/10.1090/S0002-9939-1989-0969522-4
MathSciNet review: 969522
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Abstract: We define a quotient $ [B/A]$ of bounded operators $ A$ and $ B$ on a Hilbert space $ H$ with ker $ A \subset $ ker $ B$ as the mapping $ Ax \to Bx,x \in H$, and show explicit formulae for computing quotients which correspond to sums, products, adjoints and closures of given quotients.


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DOI: https://doi.org/10.1090/S0002-9939-1989-0969522-4
Keywords: Closed operator, semiclosed operator, operator range, quotient of operators
Article copyright: © Copyright 1989 American Mathematical Society