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 that provide
models for every bounded linear operator on a separable, infinite
dimensional Hilbert space, in the sense that given an operator
on such a Hilbert space, there is and an invariant
subspace for such that the restriction of to is
similar to . 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 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.