Quotients of bounded operators

Izumino, Saichi

doi:10.1090/S0002-9939-1989-0969522-4

Quotients of bounded operators
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by Saichi Izumino

Proc. Amer. Math. Soc. 106 (1989), 427-435

DOI: https://doi.org/10.1090/S0002-9939-1989-0969522-4

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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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