Wyniki wyszukiwania

1

Spectral subspaces for the Fourier algebra

100%

Parthasarathy K., Prakash R.

Colloquium Mathematicum

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2007

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tom 108

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nr 2

179-182

EN

In this note we define and explore, à la Godement, spectral subspaces of Banach space representations of the Fourier-Eymard algebra of a (nonabelian) locally compact group.

2

On Ditkin sets

100%

Muraleedharan T. K., Parthasarathy K.

Colloquium Mathematicum

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1996

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tom 69

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nr 2

271-274

EN

In the study of spectral synthesis S-sets and C-sets (see Rudin [3]; Reiter [2] uses the terminology Wiener sets and Wiener-Ditkin sets respectively) have been discussed extensively. A new concept of Ditkin sets was introduced and studied by Stegeman in [4] so that, in Reiter's terminology, Wiener-Ditkin sets are precisely sets which are both Wiener sets and Ditkin sets. The importance of such sets in spectral synthesis and their connection to the C-set-S-set problem (see Rudin [3]) are mentioned there. In this paper we study local properties, unions and intersections of Ditkin sets. (Warning: Usually in the literature "Ditkin set" means "C-set", but we follow the terminology of Stegeman.) Our results include: (i) if each point of a closed set E has a closed relative Ditkin neighbourhood, then E is a Ditkin set; (ii) any closed countable union of Ditkin sets is a Ditkin set; (iii) if $E_1 ∩ E_2$ is a Ditkin set, then $E_1 ∩ E_2$ is a Ditkin set if and only if $E_1$ and $E_2$ are Ditkin sets; and (iv) if $E_1, E_2$ are Ditkin sets with disjoint boundaries then $E_1 ∩ E_2$ is a Ditkin set.

3

Spectral synthesis and operator synthesis

100%

Parthasarathy K., Prakash R.

Studia Mathematica

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2006

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tom 177

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nr 2

173-181

EN

Relations between spectral synthesis in the Fourier algebra A(G) of a compact group G and the concept of operator synthesis due to Arveson have been studied in the literature. For an A(G)-submodule X of VN(G), X-synthesis in A(G) has been introduced by E. Kaniuth and A. Lau and studied recently by the present authors. To any such X we associate a $V^{∞}(G)$-submodule X̂ of ℬ(L²(G)) (where $V^{∞}(G)$ is the weak-* Haagerup tensor product $L^{∞}(G) ⊗_{w*h} L^{∞}(G)$), define the concept of X̂-operator synthesis and prove that a closed set E in G is of X-synthesis if and only if $E*: = {(x,y) ∈ G × G: xy^{-1} ∈ E}$ is of X̂-operator synthesis.

Ograniczanie wyników

2 Colloquium Mathematicum

1 Studia Mathematica

3 Parthasarathy K.

2 Prakash R.

1 Muraleedharan T. K.

1 2007

1 2006

1 1996

Spectral subspaces for the Fourier algebra

On Ditkin sets

Spectral synthesis and operator synthesis