Approximate diagonals and Følner conditions for amenable group and semigroup algebras

• Autorzy: Ross Stokke
• Języki publikacji: EN

Abstrakty

EN

We study the relationship between the classical invariance properties of amenable locally compact groups G and the approximate diagonals possessed by their associated group algebras L¹(G). From the existence of a weak form of approximate diagonal for L¹(G) we provide a direct proof that G is amenable. Conversely, we give a formula for constructing a strong form of approximate diagonal for any amenable locally compact group. In particular we have a new proof of Johnson's Theorem: A locally compact group G is amenable precisely when L¹(G) is an amenable Banach algebra. Several structural Følner-type conditions are derived, each of which is shown to correctly reflect the amenability of L¹(G). We provide Følner conditions characterizing semigroups with 1-amenable semigroup algebras.

Kategorie tematyczne

• 43A07: Means on groups, semigroups, etc.; amenable groups
• 22D05: General properties and structure of locally compact groups
• 22D15: Group algebras of locally compact groups
• 43A20: L 1 -algebras on groups, semigroups, etc.

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 2004
• Tom: 164
• Numer: 2
• Strony: 139-159

Daty

wydano

2004

Twórcy

autor

Ross Stokke

• Department of Mathematics and Statistics, University of Winnipeg, 515 Portage Avenue, Winnipeg, Manitoba, Canada, R3B 2E9

Identyfikatory

DOI

10.4064/sm164-2-3