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Amenability and the second dual of a Banach algebra

100%

Gourdeau F.

Studia Mathematica

1997

tom 125

nr 1

75-81

Amenability and the Arens product are studied. Using the Arens product, derivations from A are extended to derivations from A**. This is used to show directly that A** amenable implies A amenable.

Spectrum of commutative Banach algebras and isomorphism of C*-algebras related to locally compact groups

75%

Hu Z.

Studia Mathematica

1998

tom 129

nr 3

207-223

Let A be a semisimple commutative regular tauberian Banach algebra with spectrum $Σ_A$. In this paper, we study the norm spectra of elements of $\overline{span} Σ_A$ and present some applications. In particular, we characterize the discreteness of $Σ_A$ in terms of norm spectra. The algebra A is said to have property (S) if, for all $φ ∈ \overline{\span} Σ_A \ {0}$, φ has a nonempty norm spectrum. For a locally compact group G, let $ℳ_2^{d}(Ĝ)$ denote the C*-algebra generated by left translation operators on $L^2(G)$ and $G_{d}$ denote the discrete group G. We prove that the Fourier algebra $A(G)$ has property (S) iff the canonical trace on $ℳ_2^{d}(Ĝ)$ is faithful iff $ℳ_2^{d} (Ĝ)≅ ℳ_2^{d} (Ĝ_{d})$. This provides an answer to the isomorphism problem of the two C*-algebras and generalizes the so-called "uniqueness theorem" on the group algebra $L^1(G)$ of a locally compact abelian group G. We also prove that $G_{d}$ is amenable iff G is amenable and the Figà-Talamanca-Herz algebra $A_p(G)$ has property (S) for all p.

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Fixed point properties for semigroups of nonexpansive mappings on convex sets in dual Banach spaces

75%

Lau A. T.-M., Zhang Y.

Annales Universitatis Paedagogicae Cracoviensis. Studia Mathematica

2018

tom 17

Ograniczanie wyników

2 Studia Mathematica

1 Annales Universitatis Paedagogicae Cracoviensis. Studia Mathematica

1 Gourdeau F.

1 Hu Z.

1 Lau A. T.-M.

1 Zhang Y.

1 2018

1 1998

1 1997

Wyniki wyszukiwania

Amenability and the second dual of a Banach algebra

Spectrum of commutative Banach algebras and isomorphism of C*-algebras related to locally compact groups

Fixed point properties for semigroups of nonexpansive mappings on convex sets in dual Banach spaces