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Examples of $m$-isometric tuples of operators on a Hilbert space

Caixing Gu
대한수학회 (The Korean Mathematical Society)|2018.01|대한수학회지 (Journal of the KMS)|제55권 제1호|pp. 225-251

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키워드

isometrymultivariable weighted shift$m$-isometryDrury-Arveson space
주제분류수학

초록

The $m$-isometry of a single operator in Agler and Stankus \cite{AS} was naturally generalized to the $m$-isometric tuple of several commuting operators by Gleason and Richter \cite{GR}. Some examples of $m$-isometric tuples including the recently much studied Arveson-Drury $d$-shift were given in \cite{GR}. We provide more examples of $m$-isometric tuples of operators by using sums of operators or products of operators or functions of operators. A class of $m$-isometric tuples of unilateral weighted shifts parametrized by polynomials are also constructed. The examples in Gleason and Richter \cite{GR} are then obtained by choosing some specific polynomials. This work extends partially results obtained in several recent papers on the $m$-isometry of a single operator.

Abstract

The $m$-isometry of a single operator in Agler and Stankus \cite{AS} was naturally generalized to the $m$-isometric tuple of several commuting operators by Gleason and Richter \cite{GR}. Some examples of $m$-isometric tuples including the recently much studied Arveson-Drury $d$-shift were given in \cite{GR}. We provide more examples of $m$-isometric tuples of operators by using sums of operators or products of operators or functions of operators. A class of $m$-isometric tuples of unilateral weighted shifts parametrized by polynomials are also constructed. The examples in Gleason and Richter \cite{GR} are then obtained by choosing some specific polynomials. This work extends partially results obtained in several recent papers on the $m$-isometry of a single operator.

참고문헌 (40)

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