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On Ditkin sets

T. MuraleedharanK. Parthasarathy — 1996

Colloquium Mathematicae

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...

Spectral synthesis and operator synthesis

K. ParthasarathyR. Prakash — 2006

Studia Mathematica

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...

Hall's transformation via quantum stochastic calculus

Paula CohenRobin HudsonK. ParthasarathySylvia Pulmannová — 1998

Banach Center Publications

It is well known that Hall's transformation factorizes into a composition of two isometric maps to and from a certain completion of the dual of the universal enveloping algebra of the Lie algebra of the initial Lie group. In this paper this fact will be demonstrated by exhibiting each of the maps in turn as the composition of two isometries. For the first map we use classical stochastic calculus, and in particular a stochastic analogue of the Dyson perturbation expansion. For the second map we make...

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