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Power boundedness in Banach algebras associated with locally compact groups

100%

Kaniuth E., Lau A., Ülger A.

Studia Mathematica

2014

tom 222

nr 2

165-189

Let G be a locally compact group and B(G) the Fourier-Stieltjes algebra of G. Pursuing our investigations of power bounded elements in B(G), we study the extension property for power bounded elements and discuss the structure of closed sets in the coset ring of G which appear as 1-sets of power bounded elements. We also show that L¹-algebras of noncompact motion groups and of noncompact IN-groups with polynomial growth do not share the so-called power boundedness property. Finally, we give a characterization of power bounded elements in the reduced Fourier-Stieltjes algebra of a locally compact group containing an open subgroup which is amenable as a discrete group.

Homomorphisms of commutative Banach algebras and extensions to multiplier algebras with applications to Fourier algebras

100%

Kaniuth E., Lau A., Ülger A.

Studia Mathematica

2007

tom 183

nr 1

35-62

Let A and B be semisimple commutative Banach algebras with bounded approximate identities. We investigate the problem of extending a homomorphism φ: A → B to a homomorphism of the multiplier algebras M(A) and M(B) of A and B, respectively. Various sufficient conditions in terms of B (or B and φ) are given that allow the construction of such extensions. We exhibit a number of classes of Banach algebras to which these criteria apply. In addition, we prove a polar decomposition for homomorphisms from A into A with closed range. Our results are applied to Fourier algebras of locally compact groups.

Ograniczanie wyników

2 Studia Mathematica

2 Kaniuth E.

2 Lau A.

2 Ülger A.

1 2014

1 2007

Wyniki wyszukiwania

Power boundedness in Banach algebras associated with locally compact groups

Homomorphisms of commutative Banach algebras and extensions to multiplier algebras with applications to Fourier algebras