Hostname: page-component-5cf477f64f-qls9x Total loading time: 0 Render date: 2025-04-06T08:03:30.477Z Has data issue: false hasContentIssue false
  • English
  • Français

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
Get access Rights & Permissions [Opens in a new window]

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 .

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

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

(1)Dunford, N. and Schwartz, J. T., Linear Operators, Part II. Interscience, (New York 1963).Google Scholar
(2)Edwards, R. E., Functional Analysis, Holt, Rinehart and Winston, (New York, 1965).Google Scholar
(3)Fillmore, P. A., Notes on Operator Theory. Van Nostrand Reinhold, (New York, 1970).Google Scholar
(4)Halmos, P. R. and McLaughlin, J. E., Partial Isometries, Pacific J. Math. 13 (1963) 2, 585–596.CrossRefGoogle Scholar
(5)Von Neumann, J., Allgemeine Eigenwerttheorie Hermitescher Funktionaloperatoren. Math. Ann. 102 (1929), 49–131.CrossRefGoogle Scholar
(6)Wold, H., A study in the analysis of stationary time series, (Stockholm, 1938).Google Scholar