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29/03/2000, 17:00 — 18:00 — Amphitheatre Pa1, Mathematics Building
Bernd Silbermann, Technische Universität Chemnitz

Recent Advances in Asymptotic Spectral Theory

Consider a sequence of bounded linear operators acting in some Hilbert space and suppose that this sequence tends strongly to some operator. Then it is well-known that the limiting set of the spectra of the approximating operators has almost nothing to do with the spectrum of the limit operator. Even if the convergence is uniform, the picture is not changed (Kakutani, limpotent operators). Nevertheless, in applications frequently there occur problems where one has to relate spectral quantities of the approximating operators (traces, determinants, singular values, epsilon-pseudospectra and so on) with quantities of the limit operator or something else. Nowadays there is a variety of investigations and results in that direction concerning quite different classes of operators and their approximations. It is worthwhile noticing that Toeplitz and Wiener-Hopf operators have played an outstanding role in this context: they have served as some kind of generator of ideas. This talk is devoted to the very recent progress in the field.
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The Mathematics Colloquium is a series of monthly talks organized by the Department of Mathematics of IST, aiming to be a forum for the presentation of mathematical ideas or ideas about Mathematics. The Colloquium welcomes the participation of faculty, researchers and undergraduate or graduate students, of IST or other institutions, and is seen as an opportunity of bringing together and fostering the building up of ideas in an informal atmosphere.


Organizers: Conceição Amado, Lina Oliveira e Maria João Borges.