Invariant Subspaces of Infinite Codimension for Some Nonnormal Operators

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.

Locations

• Proceedings of the American Mathematical Society - View - PDF