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In this paper, we study $m$-isometric Toeplitz operators $T_{\varphi}$ with rational symbols. We characterize $m$-isometric Toeplitz operators $T_{\varphi}$ by properties of the rational symbols $\varphi$. In addition, we give a necessary and sufficient condition for Toeplitz operators $T_{\varphi}$ with analytic symbols $\varphi$ to be $m$-expansive or $m$-contractive. Finally, we give some results for $m$-expansive and $m$-contractive Toeplitz operators $T_{\varphi}$ with trigonometric polynomial symbols $\varphi$.
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참고문헌 (18)
참고문헌 신청
J. Agler / 1990 / A disconjugacy theorem for Toeplitz operators / Amer. J. Math. 112(1):1~14
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
O. A. M. Sid Ahmed / 2010 / m-isometric operators on Banach spaces / Asian-Eur. J. Math. 3(1):1~19
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
O. A. M. Sid Ahmed / 2010 / m-isometric operators on Banach spaces / Asian-Eur. J. Math. 3(1):1~19
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