Wyniki wyszukiwania

1

Approximate weak amenability, derivations and Arens regularity of Segal algebras

100%

Ghahramani F., Lau A.

Studia Mathematica

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2005

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tom 169

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nr 2

189-205

EN

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.

2

Unitary closure and Fourier algebra of a topological group

100%

Lau A., Ludwig J.

Studia Mathematica

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2015

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tom 231

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nr 1

1-28

EN

This is a sequel to our recent work (2012) on the Fourier-Stieltjes algebra B(G) of a topological group G. We introduce the unitary closure G̅ of G and use it to study the Fourier algebra A(G) of G. We also study operator amenability and fixed point property as well as other related geometric properties for A(G).

3

A property for locally convex *-algebras related to property (T) and character amenability

81%

Chen X., Lau A., Ng C.-K.

Studia Mathematica

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2015

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tom 227

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nr 3

259-286

EN

For a locally convex *-algebra A equipped with a fixed continuous *-character ε (which is roughly speaking a generalized F*-algebra), we define a cohomological property, called property (FH), which is similar to character amenability. Let $C_{c}(G)$ be the space of continuous functions with compact support on a second countable locally compact group G equipped with the convolution *-algebra structure and a certain inductive topology. We show that $(C_{c}(G),ε_{G})$ has property (FH) if and only if G has property (T). On the other hand, many Banach algebras equipped with canonical characters have property (FH) (e.g., those defined by a nice locally compact quantum group). Furthermore, through our studies on both property (FH) and character amenablility, we obtain characterizations of property (T), amenability and compactness of G in terms of the vanishing of one-sided cohomology of certain topological algebras, as well as in terms of fixed point properties. These three sets of characterizations can be regarded as analogues of one another. Moreover, we show that G is compact if and only if the normed algebra ${f ∈ C_{c}(G): ∫_{G} f(t)dt =0}$ (under $||·||_{L¹(G)}$) admits a bounded approximate identity with the supports of all its elements being contained in a common compact set.

Ograniczanie wyników

3 Studia Mathematica

3 Lau A.

1 Chen X.

1 Ghahramani F.

1 Ludwig J.

1 Ng C.-K.

2 2015

1 2005

Approximate weak amenability, derivations and Arens regularity of Segal algebras

Unitary closure and Fourier algebra of a topological group

A property for locally convex *-algebras related to property (T) and character amenability