Colloquium 

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.