Operator Theory, Complex Analysis and Applications Seminar 

18/07/2013, 18:00 — 19:00 — Room P3.10, Mathematics Building
Carl Cowen, Indiana University-Purdue University Indianapolis, USA

Rota's Universal Operators and Invariant Subspaces in Hilbert Spaces

Rota showed, in 1960, that there are operators $T$ that provide models for every bounded linear operator on a separable, infinite dimensional Hilbert space, in the sense that given an operator $A$ on such a Hilbert space, there is $\lambda \ne 0$ and an invariant subspace $M$ for $T$ such that the restriction of $T$ to $M$ is similar to $\lambda A$. In 1969, Caradus provided a practical condition for identifying such universal operators. In this talk, we will use the Caradus theorem to exhibit a new example of a universal operator and show how it can be used to provide information about invariant subspaces for Hilbert space operators. Of course, Toeplitz operators and composition operators on the Hardy space $H^2(𝔻)$ will play a role!

This talk describes work in collaboration with Eva Gallardo-Gutiérrez, Universidad Complutense de Madrid, done there this year during the speaker's sabbatical.