| 1. |
- Alaghmandan, Mahmood, 1983, et al.
(författare)
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Projections In L1(G): The Unimodular Case
- 2016
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Ingår i: Proceedings of the American Mathematical Society. - : American Mathematical Society (AMS). - 0002-9939 .- 1088-6826. ; 144:11, s. 4929-4941
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Tidskriftsartikel (refereegranskat)abstract
- We consider the issue of describing all self-adjoint idempotents (projections) in L1(G) when G is a unimodular locally compact group. The approach is to take advantage of known facts concerning subspaces of the Fourier-Stieltjes and Fourier algebras of G and the topology of the dual space of G. We obtain an explicit description of any projection in L1(G) which happens to also lie in the coefficient space of a finite direct sum of irreducible representations. This leads to a complete description of all projections in L1(G) for G belonging to a class of groups that includes SL2(R) and all second countable almost connected nilpotent locally compact groups.
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| 2. |
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| 3. |
- Levene, Rupert, et al.
(författare)
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Schur multipliers of Cartan pairs
- 2017
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Ingår i: Proceedings of the Edinburgh Mathematical Society. - 1464-3839 .- 0013-0915. ; 60:2, s. 413-440
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Tidskriftsartikel (refereegranskat)abstract
- We define the Schur multipliers of a separable von Neumann algebra M with Cartan maximal abelian self-adjoint algebra A, generalizing the classical Schur multipliers of B(2). We characterize these as the normal A-bimodule maps on M. If M contains a direct summand isomorphic to the hyperfinite II 1 factor, then we show that the Schur multipliers arising from the extended Haagerup tensor product A⊗ehA are strictly contained in the algebra of all Schur multipliers.
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| 4. |
- Ludwig, Jean, et al.
(författare)
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Beurling-Fourier algebras on compact groups: spectral theory
- 2011
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Ingår i: Journal of Functional Analysis. - 0022-1236 .- 1096-0783. ; online
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Tidskriftsartikel (refereegranskat)abstract
- For a compact group $G$ we define the Beurling-Fourier algebra $A_\omega(G)$ on $G$ for weights $\omega$ defined on the dual $\what G$ and taking positive values. The classical Fourier algebra corresponds to the case $\omega$ is the constant weight 1. We study the Gelfand spectrum of the algebra realizing it as a subset of the complexification $G_{\mathbb C}$ defined by McKennon and Cartwright and McMullen. In many cases, such as for polynomial weights, the spectrum is simply $G$. We discuss the questions when the algebra $A_\omega(G)$ is symmetric and regular. We also obtain various results concerning spectral synthesis for $A_\omega(G)$.
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