Invariant subspaces of infinite codimension for some nonnormal operators

Clancey, Kevin

doi:10.1090/S0002-9939-1973-0308841-X

Invariant subspaces of infinite codimension for some nonnormal operators
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Proc. Amer. Math. Soc. 37 (1973), 525-528 Request permission

Abstract:

Let $\varphi \in C’[ - 1,1]$. For $f \in {L^2}( - 1,1)$ define \[ {T_\varphi }f(s) = sf(s) + \frac {{\varphi (s)}}{\pi }\int _{ - 1}^{1 \ast } {\frac {{\bar \varphi f(t)}}{{s - t}}dt.} \] Our main result says ${T_\varphi }$ has invariant subspaces of infinite co-dimension.

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Integral equations