- Tytuł:
- Spectrum of commutative Banach algebras and isomorphism of C*-algebras related to locally compact groups
- Autorzy:
- Hu, Zhiguo
- Powiązania:
- https://bibliotekanauki.pl/articles/1218426.pdf
- Data publikacji:
- 1998
- Wydawca:
- Polska Akademia Nauk. Instytut Matematyczny PAN
- Tematy:
-
spectrum
synthesizable ideal
locally compact group
Fourier algebra
Figà-Talamanca-Herz algebra
amenability - Opis:
- 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.
- Źródło:
-
Studia Mathematica; 1998, 129, 3; 207-223
0039-3223 - Pojawia się w:
- Studia Mathematica
- Dostawca treści:
- Biblioteka Nauki
Artykuł