01/15/2018 - 4:15pm

01/15/2018 - 5:15pm

Speaker:

George Exner (Bucknell)

Abstract:

Two standard presentations of Hilbert space are as a space of square summable complex-valued sequences and as square integrable analytic functions on the open unit disk $\mathbb{D}$. A standard example of a bounded linear operator on the first is a weighted shift, and on the second the composition operator $C_\varphi$ associated with an analytic function $\varphi$ mapping $\mathbb{D}$ to $\mathbb{D}$. In work joint with Isabelle Chalendar, we exhibit some composition operators with invariant subspaces on which they act as weighted shifts. Consideration of the subnormality of the shift (an ``operator theory question'') gives information about a fixed point of $\varphi$ (a ``function theory question''), and the results yield also some intriguing complex geometry which we do not understand well.

Where:

Emmy Noether Rm
Millikan 1021
Pomona College

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