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Let $p\ge 1$ be a real number. A tuple ${T}=(T_1,\ldots ,T_n)$ of commuting bounded linear operators on a Banach space $X$ is called an $\ell^p$-spherical isometry if $\sum_{i=1} ^n \|T_ix\|^p =\|x\|^p$ for all $x\in X$. The tuple $T$ is called a toral isometry if each $T_i$ is an isometry. By a result of Ansari, Hedayatian, Khani-Robati and Moradi, for every $n\ge1$, there is a supercyclic $\ell^2$-spherical isometric $n$-tuple on ${\mathbb C}^{n}$ but there is no supercyclic $\ell^2$-spherical isometry on an infinite-dimensional Hilbert space. In this article, we investigate the supercyclicity of $\ell^p$-spherical isometries and toral isometries on Banach spaces. Also, we introduce the notion of semi-commutative tuples and we show that the Banach spaces $\ell^p$ ($1\le p<\infty$) support supercyclic $\ell^p$-spherical isometric semi-commutative tuples. As a result, all separable infinite-dimensional complex Hilbert spaces support supercyclic spherical isometric semi-commutative tuples.
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참고문헌 (9)
참고문헌 신청
S. I. Ansari / 1997 / Some properties of cyclic operators / Acta Sci. Math. (Szeged) 63(1-2):195~207
Mohammad Ansari / 2015 / SUPERCYCLICITY OF JOINT ISOMETRIES / 대한수학회보 52(5):1481~1487
A. Athavale / 1990 / On the intertwining of joint isometries / J. Operator Theory 23(2):339~350
N. S. Feldman / 2008 / Hypercyclic tuples of operators and somewhere dense orbits / J. Math. Anal. Appl 346(1):82~98
H. M. Hilden / 1974 / Some cyclic and non-cyclic vectors of certain operators / Indiana Univ. Math. J 23:557~565
Mohammad Ansari / 2015 / SUPERCYCLICITY OF JOINT ISOMETRIES / 대한수학회보 52(5):1481~1487
A. Athavale / 1990 / On the intertwining of joint isometries / J. Operator Theory 23(2):339~350
N. S. Feldman / 2008 / Hypercyclic tuples of operators and somewhere dense orbits / J. Math. Anal. Appl 346(1):82~98
H. M. Hilden / 1974 / Some cyclic and non-cyclic vectors of certain operators / Indiana Univ. Math. J 23:557~565
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