Harmonic Analysis of Operators on Hilbert Space

Abstract

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Multiplication operators on the Bergman space via the Hardy space of the bidisk

“…Given a pure isometry U on a Hilbert space H, the classical Wold decomposition theorem [19] states that…”

An introduction to Rota’s universal operators: properties, old and new examples and future issues

“…Theorem (see the classical book [18], for instance), such an operator can be represented as a block matrix on H D …”

A short introduction to de Branges–Rovnyak spaces

“…This will show that in the extreme case the de Branges-Rovnyak spaces are model spaces for a large class of operators. The theorem below (as well as its proof) is in fact a particular case of the much more general analysis of contractions done in the Sz.Nagy-Foias theory (see [24]). Here we have adapted the argument to a "minimal" self-contained form.…”

“…They have been in the shade for a few decades, as the much more popular and well developed model theory of Sz-Nagy and Foias [24] has gained the upper hand. It is known to experts that the two theories are equivalent, and we thought that a justification of the study of de Branges-Rovnyak spaces should include some presentation of their role as model spaces.…”

“…Theorem 3.2 is a particular case of the general Sz.-Nagy-Foias theory of contractions (see, for instance, the revised edition [24] of the original monography); one can find it also in [19].…”