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Spectral approximation for Segal-Bargmann space Toeplitz operators

Albrecht BöttcherHartmut Wolf — 1997

Banach Center Publications

Let A stand for a Toeplitz operator with a continuous symbol on the Bergman space of the polydisk N or on the Segal-Bargmann space over N . Even in the case N = 1, the spectrum Λ(A) of A is available only in a few very special situations. One approach to gaining information about this spectrum is based on replacing A by a large “finite section”, that is, by the compression A n of A to the linear span of the monomials z 1 k 1 . . . z N k N : 0 k j n . Unfortunately, in general the spectrum of A n does not mimic the spectrum of A as...

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