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On Compact Perturbations of Operators

Published online by Cambridge University Press:  20 November 2018

Joel Anderson
Joel Anderson*
Affiliation:
California Institute of Technology, Pasadena, California
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Recently R. G. Douglas showed [4] that if V is a nonunitary isometry and U is a unitary operator (both acting on a complex, separable, infinite dimensional Hilbert space ), then V — K is unitarily equivalent to V ⊕ U (acting on ⊕ ) where K is a compact operator of arbitrarily small norm. In this note we shall prove a much more general theorem which seems to indicate "why" Douglas' theorem holds (and which yields Douglas' theorem as a corollary).

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 26 , Issue 1 , February 1974 , pp. 247 - 250
Copyright
Copyright © Canadian Mathematical Society 1974

References

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