Characterizations of amenable representations of compact groups

Michael Yin-Hei Cheng

The search session has expired. Please query the service again.

Displaying similar documents to “Characterizations of amenable representations of compact groups”

Amenability of Banach and C*-algebras on locally compact groups

A. Lau, R. Loy, G. Willis (1996)

Studia Mathematica

Similarity:

Several results are given about the amenability of certain algebras defined by locally compact groups. The algebras include the C*-algebras and von Neumann algebras determined by the representation theory of the group, the Fourier algebra A(G), and various subalgebras of these.

Fixed point characterization of left amenable Lau algebras.

Nasr-Isfahani, R. (2004)

International Journal of Mathematics and Mathematical Sciences

Similarity:

Approximate weak amenability, derivations and Arens regularity of Segal algebras

Fereidoun Ghahramani, Anthony To-Ming Lau (2005)

Studia Mathematica

Similarity:

We continue our study of derivations, multipliers, weak amenability and Arens regularity of Segal algebras on locally compact groups. We also answer two questions on Arens regularity of the Lebesgue-Fourier algebra left open in our earlier work.

Inner amenability of Lau algebras

R. Nasr-Isfahani (2001)

Archivum Mathematicum

Similarity:

A concept of amenability for an arbitrary Lau algebra called inner amenability is introduced and studied. The inner amenability of a discrete semigroup is characterized by the inner amenability of its convolution semigroup algebra. Also, inner amenable Lau algebras are characterized by several equivalent statements which are similar analogues of properties characterizing left amenable Lau algebras.

Geometry of the Fourier Algebras and Locally Compact Groups with Atomic Unitary Representations.

Keith F. Taylor (1983)

Mathematische Annalen

Similarity:

Isometries of the unitary groups in C*-algebras

Osamu Hatori (2014)

Studia Mathematica

Similarity:

We give a complete description of the structure of surjective isometries between the unitary groups of unital C*-algebras. While any surjective isometry between the unitary groups of von Neumann algebras can be extended to a real-linear Jordan *-isomorphism between the relevant von Neumann algebras, this is not the case for general unital C*-algebras. We show that the unitary groups of two C*-algebras are isomorphic as metric groups if and only if the C*-algebras are isomorphic in the...

On derivations and crossed homomorphisms

Viktor Losert (2010)

Banach Center Publications

Similarity:

We discuss some results about derivations and crossed homomorphisms arising in the context of locally compact groups and their group algebras, in particular, L¹(G), the von Neumann algebra VN(G) and actions of G on related algebras. We answer a question of Dales, Ghahramani, Grønbæk, showing that L¹(G) is always permanently weakly amenable. Then we show that for some classes of groups (e.g. IN-groups) the homology of L¹(G) with coefficients in VN(G) is trivial. But this is no longer...

Disjointness preserving mappings between Fourier algebras

Juan J. Font (1998)

Colloquium Mathematicae

Similarity:

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

E. Kaniuth, A. T. Lau, A. Ülger (2007)

Studia Mathematica

Similarity:

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...

Analysis on a class of Banach algebras with applications to harmonic analysis on locally compact groups and semigroups

Anthony To-Ming Lau (1983)

Fundamenta Mathematicae

Similarity:

Convolutions on compact groups and Fourier algebras of coset spaces

Brian E. Forrest, Ebrahim Samei, Nico Spronk (2010)

Studia Mathematica

Similarity:

We study two related questions. (1) For a compact group G, what are the ranges of the convolution maps on A(G × G) given for u,v in A(G) by u × v ↦ u*v̌ (v̌(s) = v(s^-1)) and u × v ↦ u*v? (2) For a locally compact group G and a compact subgroup K, what are the amenability properties of the Fourier algebra of the coset space A(G/K)? The algebra A(G/K) was defined and studied by the first named author. In answering the first question, we obtain, for compact groups which...

Approximate diagonals and Følner conditions for amenable group and semigroup algebras

Ross Stokke (2004)

Studia Mathematica

Similarity:

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...

Subalgebras generated by extreme points in Fourier-Stieltjes algebras of locally compact groups

Michael Yin-hei Cheng (2011)

Studia Mathematica

Similarity:

Let G be a locally compact group, G* be the set of all extreme points of the set of normalized continuous positive definite functions of G, and a(G) be the closed subalgebra generated by G* in B(G). When G is abelian, G* is the set of Dirac measures of the dual group Ĝ, and a(G) can be identified as l¹(Ĝ). We study the properties of a(G), particularly its spectrum and its dual von Neumann algebra.

Amenability for dual Banach algebras

V. Runde (2001)

Studia Mathematica

Similarity:

We define a Banach algebra 𝔄 to be dual if 𝔄 = (𝔄⁎)* for a closed submodule 𝔄⁎ of 𝔄*. The class of dual Banach algebras includes all W*-algebras, but also all algebras M(G) for locally compact groups G, all algebras ℒ(E) for reflexive Banach spaces E, as well as all biduals of Arens regular Banach algebras. The general impression is that amenable, dual Banach algebras are rather the exception than the rule. We confirm this impression. We first show that under certain conditions...

Power boundedness in Banach algebras associated with locally compact groups

E. Kaniuth, A. T. Lau, A. Ülger (2014)

Studia Mathematica

Similarity:

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...

Dual Banach algebras and Connes-amenability.

Uygul, Faruk (2008)

Acta Mathematica Academiae Paedagogicae Nyí regyháziensis. New Series [electronic only]

Similarity:

On weak Agassiz systems of algebras

Ewa Graczyńska, Andrzej Wroński (1978)

Colloquium Mathematicum

Similarity:

Dual spaces and translation invariant means on group von Neumann algebras

Michael Yin-Hei Cheng (2014)

Studia Mathematica

Similarity:

Let G be a locally compact group. Its dual space, G*, is the set of all extreme points of the set of normalized continuous positive definite functions of G. In the early 1970s, Granirer and Rudin proved independently that if G is amenable as discrete, then G is discrete if and only if all the translation invariant means on $L^{\infty} (G)$ are topologically invariant. In this paper, we define and study G*-translation operators on VN(G) via G* and investigate the problem of the existence of G*-translation...