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A Note on the Adjoint of the Product of Operators

Published online by Cambridge University Press:  20 November 2018

Chia-Shiang Lin
Chia-Shiang Lin*
Affiliation:
Queen's University, Kingston, Ontario
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Cordes and Labrousse ([2] p. 697), and Kaniel and Schechter ([6] p. 429) showed that if S and T are domain-dense closed linear operators on a Hilbert space H into itself, the range of S is closed in H and the codimension of the range of S is finite, then, (TS)* = S*T*. With a somewhat different approach and more restricted condition on S, the same assertion was obtained by Holland [5] recently, that S is a bounded everywhere-defined linear operator whose range is a closed subspace of finite codimension in H.

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 13 , Issue 1 , March 1970 , pp. 39 - 45
Copyright
Copyright © Canadian Mathematical Society 1970

References

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