m-isometries on Banach spaces

被引：66

作者：

Bayart, Frederic ^{[1
,2
]}

机构：

[1] Clermont Univ, Univ Blaise Pascal, Math Lab, F-63000 Clermont Ferrand, France

[2] CNRS, UMB 6620, Math Lab, F-63177 Aubiere, France

来源：

MATHEMATISCHE NACHRICHTEN | 2011年 / 284卷 / 17-18期

关键词：

Supercyclic operators; m-isometry; N-SUPERCYCLIC OPERATORS; HILBERT-SPACE; TRANSFORMATIONS;

D O I：

10.1002/mana.200910029

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We introduce the notion of an m-isometry of a Banach space, following a definition of Agler and Stankus in the Hilbert space setting. We give a first approach to the general theory of these maps. Then, we focus on the dynamics of m-isometries, showing that they are never N-supercyclic. This result is new even on a Hilbert space, and even for isometries on a general Banach space.

引用

页码：2141 / 2147

页数：7

共 9 条

[1] M-ISOMETRIC TRANSFORMATIONS OF HILBERT-SPACE .1.
AGLER, J
STANKUS, M
[J]. INTEGRAL EQUATIONS AND OPERATOR THEORY, 1995, 21 (04) : 383 - 429
[2] m-Isometric transformations of Hilbert space .3.
Agler, J
Stankus, H
[J]. INTEGRAL EQUATIONS AND OPERATOR THEORY, 1996, 24 (04) : 379 - 421
[3] M-ISOMETRIC TRANSFORMATIONS OF HILBERT-SPACE .2.
AGLER, J
STANKUS, M
[J]. INTEGRAL EQUATIONS AND OPERATOR THEORY, 1995, 23 (01) : 1 - 48
[4] Ansari SI., 1997, Acta Sci. Math. (Szeged), V63, P195
[5] Bayart F., 2009, CAMB TRACT MATH, V179
[6] BERMUDEZ T, 2009, ORBIT M ISOMETRY
[7] Some properties of N-supercyclic operators
Bourdon, PS
Feldman, NS
Shapiro, JH
[J]. STUDIA MATHEMATICA, 2004, 165 (02) : 135 - 157
[8] n-supercyclic operators
Feldman, NS
[J]. STUDIA MATHEMATICA, 2002, 151 (02) : 141 - 159
[9] Hyperinvariant subspaces of operators with non-vanishing orbits
Kérchy, L
[J]. PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 1999, 127 (05) : 1363 - 1370

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