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Approximate diagonals and Følner conditions for amenable group and semigroup algebras

100%

Stokke R.

Studia Mathematica

2004

tom 164

nr 2

139-159

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.

Contractive homomorphisms of measure algebras and Fourier algebras

100%

Stokke R.

Studia Mathematica

2012

tom 209

nr 2

135-150

We show that the dual version of our factorization [J. Funct. Anal. 261 (2011)] of contractive homomorphisms φ: L¹(F) → M(G) between group/measure algebras fails to hold in the dual, Fourier/Fourier-Stieltjes algebra, setting. We characterize the contractive w*-w* continuous homomorphisms between measure algebras and (reduced) Fourier-Stieltjes algebras. We consider the problem of describing all contractive homomorphisms φ: L¹(F) → L¹(G).

Ograniczanie wyników

2 Studia Mathematica

2 Stokke R.

1 2012

1 2004

Wyniki wyszukiwania

Approximate diagonals and Følner conditions for amenable group and semigroup algebras

Contractive homomorphisms of measure algebras and Fourier algebras