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Banach空间上的强混合算子 被引量：5

Strongly Mixing Operators on Banach Space
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摘要 1999年,L．B．Gonzalez 证明了任意无限维可分 Banach 空间上存在拓扑传递的有界线性算子．这个结果肯定地回答了 S．Rolewicz 提出的问题．本文证明了由 L．B．Gonzalez 所给出的算子实际上是强混合的,同时,对加权移位算子的混合性利用权序列进行了刻划并指出任意无限维可分 Hilbert 空间上存在弱混合而非强混合的有界线性算子． In 1999, L.Bernal-Gonzalez showed that there exists a topologically transitive bounded operator on any infinite-dimensional separable Banach space. This result affirmatively solves S.Rolewicz＇s problem. This paper shows the operator given by L.Bernal-Gonzalez is in fact strongly mixing, and also characterize strongly mixing weighted shifts in terms of their weight sequence and show that any infinite-dimensional separable Hilbert space supports a weakly mixing but not strongly mixing operator.
作者 姚玉武 史恩慧 周友成
机构地区 苏州大学数学科学学院
出处 《数学年刊（A辑）》 CSCD 北大核心 2006年第2期189-196,共8页 Chinese Annals of Mathematics
关键词 拓扑传递性 弱混合 强混合 加权移位算予 BANACH空间 Topological transitivity, Weak mixing, Strong mixing, Weighted shift, Banach space
分类号 O177.2 [理学—基础数学]
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参考文献11

  • 1Ansari S.I.,Existence of hypercyclic operators on topological vectors spaces[J].J.Funct.Anal.,1997,148:384-390.
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同被引文献22

  • 1Rolewicz S.On orbits of elements[J].Studia Math,1969,32:17-22.
  • 2Ansari S I.Existence of hypercyclic operators on topological vectors spaces[J].J Funct Anal,1997,148:384-390.
  • 3Bernal-Gonz(a)lez L.On hypercyclic operators on Banach space[J].Proc Amer Math Soc,1999,127:1003-1010.
  • 4Bonet J,Peris A.Hypercyclic operators on non-normable Fr(e)chet spaces[J].J Funct Anal,1998,159:587-595.
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  • 7Bermudez T,Bonilla A,Martinon A.On the existence of chaotic and hypercyclic semigroups on Banach spaces[J].Proc Amer Math Soc,2002,131:2435-2441.
  • 8Ovsepian R I,Pelczynski A.On the existence of a fundamental total and bounded biorthogonal sequence in every separable Banach space,and related constructions of uniformly bouneded orthonormal systems in L2[J].Studia Math,1975,54:149-159.
  • 9Ovsepian R I,Pelczynski A. On the existence of a fundamental total and bounded biorthogonal sequence in every separable Banach space, and related constructions of uniformly bouneded orthonormal systems in L2 [J]. Studia Math, 1975, 54:49 - 159.
  • 10Pazy A. Semigroups of Linear Operators and Applications to Partial Differential Equations [ M ]. Springer - Verlag, New York Berlin Heidelberg Tokyo.

引证文献5

二级引证文献3

数学年刊（A辑）
2006年 第2期

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