Uniformly cyclic vectors

• Autorzy: Joseph Rosenblatt
• Języki publikacji: EN

Abstrakty

EN

A group acting on a measure space (X,β,λ) may or may not admit a cyclic vector in $L_{∞}(X)$. This can occur when the acting group is as big as the group of all measure-preserving transformations. But it does not occur, even though there is no cardinality obstruction to it, for the regular action of a group on itself. The connection of cyclic vectors to the uniqueness of invariant means is also discussed.

Kategorie tematyczne

• 43A15: L p -spaces and other function spaces on groups, semigroups, etc.
• 43A07: Means on groups, semigroups, etc.; amenable groups
• 43A65: Representations of groups, semigroups, etc.
• 43A77: Analysis on general compact groups

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Colloquium Mathematicum
• Rocznik: 2006
• Tom: 104
• Numer: 1
• Strony: 21-32

Daty

wydano

2006

Twórcy

autor

Joseph Rosenblatt

• Department of Mathematics, University of Illinois at, Urbana, Urbana, IL 61801, U.S.A.

Identyfikatory

DOI

10.4064/cm104-1-2