Mathematics Colloquia and Seminars

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One surprising feature of operator theory on infinite dimensional Hilbert space is that operators can possess an open set of eigenvalues. Almost thirty years ago the speaker and M. Cowen developed a method for studying such operators using concepts and techniques from complex geometry. The operators studied were shown to be locally determined in the sense that restrictions of the operators to finite dimensional subspaces of generalized eigenvectors determined them up to unitary equivalence. While the statement of this result was completely in the language of operator theory, the methods involve complex geometry.

In this talk, we will describe and explain these results including generalizations of them to multivariate operator theory in which, again, the language of operator theory is used but complex geometric methods, this time in several variables, are the key. Throughout the talk, there will be an emphasis on examples.