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Departamento de Matemática Técnico Técnico

Seminário de Teoria de Operadores, Análise Complexa e Aplicações  RSS

18/07/2013, 18:00 — 19:00 — Sala P3.10, Pavilhão de Matemática
, 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 λ0 and an invariant subspace M for T such that the restriction of T to M is similar to λA. 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.


Seminário organizado no contexto do projecto PTDC/MAT/121837/2010.

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