Wyniki wyszukiwania

1

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

100%

Hu Z.

Studia Mathematica

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1998

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tom 129

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nr 3

207-223

EN

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.

2

Extreme non-Arens regularity of quotients of the Fourier algebra A(G)

100%

Hu Z.

Colloquium Mathematicum

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1997

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tom 72

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nr 2

237-249

3

Inductive extreme non-Arens regularity of the Fourier algebra A(G)

100%

Hu Z.

Studia Mathematica

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2002

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tom 151

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nr 3

247-264

EN

Let G be a non-discrete locally compact group, A(G) the Fourier algebra of G, VN(G) the von Neumann algebra generated by the left regular representation of G which is identified with A(G)*, and WAP(Ĝ) the space of all weakly almost periodic functionals on A(G). We show that there exists a directed family ℋ of open subgroups of G such that: (1) for each H ∈ ℋ, A(H) is extremely non-Arens regular; (2) $VN(G) = ⋃_{H∈ℋ} VN(H)$ and $VN(G)/WAP(Ĝ) = ⋃_{H∈ℋ} [VN(H)/WAP(Ĥ)]$; (3) $A(G) = ⋃_{H∈ℋ} A(H)$ and it is a WAP-strong inductive union in the sense that the unions in (2) are strongly compatible with it. Furthermore, we prove that the family {A(H): H ∈ ℋ } of Fourier algebras has a kind of inductively compatible extreme non-Arens regularity.

4

Module maps over locally compact quantum groups

51%

Hu Z., Neufang M., Ruan Z.-J.

Studia Mathematica

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2012

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tom 211

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nr 2

111-145

EN

We study locally compact quantum groups 𝔾 and their module maps through a general Banach algebra approach. As applications, we obtain various characterizations of compactness and discreteness, which in particular generalize a result by Lau (1978) and recover another one by Runde (2008). Properties of module maps on $L_{∞}(𝔾)$ are used to characterize strong Arens irregularity of L₁(𝔾) and are linked to commutation relations over 𝔾 with several double commutant theorems established. We prove the quantum group version of the theorems by Young (1973), Lau (1981), and Forrest (1991) regarding Arens regularity of the group algebra L₁(G) and the Fourier algebra A(G). We extend the classical Eberlein theorem on the inclusion B(G) ⊆ WAP(G) to all locally compact quantum groups.

Ograniczanie wyników

3 Studia Mathematica

1 Colloquium Mathematicum

4 Hu Z.

1 Neufang M.

1 Ruan Z.-J.

1 2012

1 2002

1 1998

1 1997

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

Extreme non-Arens regularity of quotients of the Fourier algebra A(G)

Inductive extreme non-Arens regularity of the Fourier algebra A(G)

Module maps over locally compact quantum groups