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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Invariant subspaces of infinite codimension for some nonnormal operators


Author: Kevin Clancey
Journal: Proc. Amer. Math. Soc. 37 (1973), 525-528
MSC: Primary 47B20; Secondary 45E05, 47A15
MathSciNet review: 0308841
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Abstract: Let $ \varphi \in C'[ - 1,1]$. For $ f \in {L^2}( - 1,1)$ define

$\displaystyle {T_\varphi }f(s) = sf(s) + \frac{{\varphi (s)}}{\pi }\int_{ - 1}^{1 \ast } {\frac{{\bar \varphi f(t)}}{{s - t}}dt.} $

Our main result says $ {T_\varphi }$ has invariant subspaces of infinite co-dimension.

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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1973-0308841-X
PII: S 0002-9939(1973)0308841-X
Keywords: Hyponormal operator, singular integral, invariant subspaces
Article copyright: © Copyright 1973 American Mathematical Society