Locally equicontinuous dynamical systems

• Autorzy: Eli Glasner , Benjamin Weiss
• Języki publikacji: EN

Abstrakty

EN

A new class of dynamical systems is defined, the class of "locally equicontinuous systems" (LE). We show that the property LE is inherited by factors as well as subsystems, and is closed under the operations of pointed products and inverse limits. In other words, the locally equicontinuous functions in $l_{∞}(ℤ)$ form a uniformly closed translation invariant subalgebra. We show that WAP ⊂ LE ⊂ AE, where WAP is the class of weakly almost periodic systems and AE the class of almost equicontinuous systems. Both of these inclusions are proper. The main result of the paper is to produce a family of examples of LE dynamical systems which are not WAP.

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Colloquium Mathematicum
• Rocznik: 2000
• Tom: 84/85
• Numer: 2
• Strony: 345-361

Daty

wydano

2000

otrzymano

1999-08-13

poprawiono

1999-10-19

Twórcy

autor

Eli Glasner

• Mathematics Department, Tel Aviv University, Tel Aviv, Israel

autor

Benjamin Weiss

• Mathematics Institute, Hebrew University of Jerusalem, Jerusalem, Israel

Bibliografia

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