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<p>We investigate the topological entropy of operators. More precisely, in the Banach space setting, we show that compact operators have finite entropy, which depends solely on their point spectrum. Moreover, for operators on <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(F\)</EquationSource> <EquationSource Format="MATHML"><math> <mi>F</mi> </math></EquationSource> </InlineEquation>-spaces, we explore the relationship between the specification property and entropy. In particular, we show that the specification property implies infinite topological entropy, while the operator specification property implies positive entropy. We also show that the invariance principle fails for the class of compact operators.</p>

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Entropy for compact operators and results on entropy and specification

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2026年2月20日

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  • Paulo Lupatini,
  • Felipe Carvalho Silva,
  • Régis Varão

摘要

We investigate the topological entropy of operators. More precisely, in the Banach space setting, we show that compact operators have finite entropy, which depends solely on their point spectrum. Moreover, for operators on \(F\) F -spaces, we explore the relationship between the specification property and entropy. In particular, we show that the specification property implies infinite topological entropy, while the operator specification property implies positive entropy. We also show that the invariance principle fails for the class of compact operators.