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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.
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참고문헌 (40)
참고문헌 신청
J. Agler / 1982 / The Arveson extension theorem and coanalytic models / Integral Equations Operator Theory 5(1):608~631
J. Agler / 1998 / Classification of hereditary matrices / Linear Algebra Appl. 274:125~160
J. Agler / 1995 / m-Isometric transformations of Hilbert space, I / Integral Equations Operator Theory 21(4):383~429
J. Agler / 1995 / m-isometric transformations of Hilbert space, II / Integral Equations Operator Theory 23(1):1~48
J. Agler / 1996 / m-isometric transformations of Hilbert space, III / Integral Equations Operator Theory 24(4):379~421
J. Agler / 1998 / Classification of hereditary matrices / Linear Algebra Appl. 274:125~160
J. Agler / 1995 / m-Isometric transformations of Hilbert space, I / Integral Equations Operator Theory 21(4):383~429
J. Agler / 1995 / m-isometric transformations of Hilbert space, II / Integral Equations Operator Theory 23(1):1~48
J. Agler / 1996 / m-isometric transformations of Hilbert space, III / Integral Equations Operator Theory 24(4):379~421
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