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Partial isometries which are sums of shifts

Published online by Cambridge University Press:  24 October 2008

B. Fishel
B. Fishel
Affiliation:
Westfield College, University of London
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Extract

Let denote a Hilbert space (real or complex), with inner product (|). In order to present our notation, we recall that if is a vector subspace of (and ‘vector sub-spaces’ will always be closed), with orthocomplement , a partial isometry V with initial domain is a linear operator in which preserves length, and so inner-product, in and is zero in is the final domain of V, and it is easy to verify that V*, the adjoint operator, is also a partial isometry, with initial domain and final domain .

Information

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 78 , Issue 1 , July 1975 , pp. 107 - 110
Copyright
Copyright © Cambridge Philosophical Society 1975

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References

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