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Weak spectral synthesis in Fourier algebras of coset spaces

100%

Kaniuth E.

Studia Mathematica

2010

tom 197

nr 3

229-246

Let G be a locally compact group, K a compact subgroup of G and A(G/K) the Fourier algebra of the coset space G/K. Applying results from [E. Kaniuth, Weak spectral synthesis in commutative Banach algebras, J. Funct. Anal. 254 (2008), 987-1002], we establish injection and localization theorems relating weak spectral sets and weak Ditkin sets for A(G/K) to such sets for A(H/H ∩ K), where H is a closed subgroup of G. We also prove some results towards the analogue of Malliavin's theorem for weak spectral synthesis in A(G/K) and give illustrating examples.

Stable rank and real rank of compact transformation group C*-algebras

63%

Archbold R., Kaniuth E.

Studia Mathematica

2006

tom 175

nr 2

103-120

Let (G,X) be a transformation group, where X is a locally compact Hausdorff space and G is a compact group. We investigate the stable rank and the real rank of the transformation group C*-algebra C₀(X)⋊ G. Explicit formulae are given in the case where X and G are second countable and X is locally of finite G-orbit type. As a consequence, we calculate the ranks of the group C*-algebra C*(ℝⁿ ⋊ G), where G is a connected closed subgroup of SO(n) acting on ℝⁿ by rotation.

Ograniczanie wyników

2 Studia Mathematica

2 Kaniuth E.

1 Archbold R.

1 2010

1 2006

Wyniki wyszukiwania

Weak spectral synthesis in Fourier algebras of coset spaces

Stable rank and real rank of compact transformation group C*-algebras