On the structure of selfadjoint Toeplitz operators with rational matrix symbols

Rodman, Leiba

doi:10.1090/S0002-9939-1984-0760931-0

On the structure of selfadjoint Toeplitz operators with rational matrix symbols
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Proc. Amer. Math. Soc. 92 (1984), 487-494 Request permission

Abstract:

Selfadjoint Toeplitz operators with rational matrix symbols are studied using a general result concerning functions $(T{(z)^{ - 1}}x,y)$ where $T(z)$ is a polynomial family of Toeplitz operators with rational matrix symbols. It is proved that, apart from a finite number of points, these functions can be continued analytically across the boundary of the resolvent set of $T(z)$, for a dense set of $x$’s and $y$’s. This implies piecewise analyticity of the spectral measure $(Ex,x)$ of selfadjoint Toeplitz operators with rational matrix symbol, for a dense set of $x$’s.

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Functional analysis