## Composition operators and weighted shifts

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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