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Connes amenability-like properties

Amin Mahmoodi (2014)

Studia Mathematica

We introduce and study the notions of w*-approximate Connes amenability and pseudo-Connes amenability for dual Banach algebras. We prove that the dual Banach sequence algebra ℓ¹ is not w*-approximately Connes amenable. We show that in general the concepts of pseudo-Connes amenability and Connes amenability are distinct. Moreover the relations between these new notions are also discussed.

Contractive homomorphisms of measure algebras and Fourier algebras

Ross Stokke (2012)

Studia Mathematica

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).

Convolution operators on the dual of hypergroup algebras

Ali Ghaffari (2003)

Commentationes Mathematicae Universitatis Carolinae

Let X be a hypergroup. In this paper, we define a locally convex topology β on L ( X ) such that ( L ( X ) , β ) * with the strong topology can be identified with a Banach subspace of L ( X ) * . We prove that if X has a Haar measure, then the dual to this subspace is L C ( X ) * * = cl { F L ( X ) * * ; F has compact carrier}. Moreover, we study the operators on L ( X ) * and L 0 ( X ) which commute with translations and convolutions. We prove, among other things, that if wap ( L ( X ) ) is left stationary, then there is a weakly compact operator T on L ( X ) * which commutes with convolutions if and...

Decomposable multipliers and applications to harmonic analysis

Kjeld Laursen, Michael Neumann (1992)

Studia Mathematica

For a multiplier on a semisimple commutative Banach algebra, the decomposability in the sense of Foiaş will be related to certain continuity properties and growth conditions of its Gelfand transform on the spectrum of the multiplier algebra. If the multiplier algebra is regular, then all multipliers will be seen to be decomposable. In general, an important tool will be the hull-kernel topology on the spectrum of the typically nonregular multiplier algebra. Our investigation involves various closed...

Derivations into iterated duals of Banach algebras

H. Dales, F. Ghahramani, N. Grønbæek (1998)

Studia Mathematica

We introduce two new notions of amenability for a Banach algebra A. The algebra A is n-weakly amenable (for n ∈ ℕ) if the first continuous cohomology group of A with coefficients in the n th dual space A ( n ) is zero; i.e., 1 ( A , A ( n ) ) = 0 . Further, A is permanently weakly amenable if A is n-weakly amenable for each n ∈ ℕ. We begin by examining the relations between m-weak amenability and n-weak amenability for distinct m,n ∈ ℕ. We then examine when Banach algebras in various classes are n-weakly amenable; we study...

Extension de la catégorie des algèbres de Kac

M. Enock, J. M. Schwartz (1986)

Annales de l'institut Fourier

On munit la classe des algèbres de Kac d’une nouvelle classe de morphismes, stable par dualité. Cela permet de rendre compte, dans les cas abélien ou symétrique, de la catégorie des groupes localement compacts munis des morphismes continus de groupe. Le lien avec les morphismes précédemment définis et beaucoup plus restrictifs est établi.

Good weights for weighted convolution algebras

Sandy Grabiner (2010)

Banach Center Publications

Weighted convolution algebras L¹(ω) on R⁺ = [0,∞) have been studied for many years. At first results were proved for continuous weights; and then it was shown that all such results would also hold for properly normalized right continuous weights. For measurable weights, it was shown that one could construct a properly normalized right continuous weight ω' with L¹(ω') = L¹(ω) with an equivalent norm. Thus all algebraic and norm-topology results remained true for measurable weights. We now show that,...

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