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Unitary closure and Fourier algebra of a topological group

100%
Lau A., Ludwig J.
Studia Mathematica
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2015
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tom 231
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nr 1
1-28
EN
This is a sequel to our recent work (2012) on the Fourier-Stieltjes algebra B(G) of a topological group G. We introduce the unitary closure G̅ of G and use it to study the Fourier algebra A(G) of G. We also study operator amenability and fixed point property as well as other related geometric properties for A(G).
2
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Growth and smooth spectral synthesis in the Fourier algebras of Lie groups

100%
Ludwig J., Turowska L.
Studia Mathematica
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2006
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tom 176
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nr 2
139-158
EN
Let G be a Lie group and A(G) the Fourier algebra of G. We describe sufficient conditions for complex-valued functions to operate on elements u ∈ A(G) of certain differentiability classes in terms of the dimension of the group G. Furthermore, generalizing a result of Kirsch and Müller [Ark. Mat. 18 (1980), 145-155] we prove that closed subsets E of a smooth m-dimensional submanifold of a Lie group G having a certain cone property are sets of smooth spectral synthesis. For such sets we give an estimate of the degree of nilpotency of the quotient algebra $I_{A}(E)/J_{A}(E)$, where $I_{A}(E)$ and $J_{A}(E)$ are the largest and the smallest closed ideals in A(G) with hull E.
3
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Minimal ideals of group algebras

100%
Alexander D., Ludwig J.
Studia Mathematica
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2004
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tom 160
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nr 3
205-229
EN
We first study the behavior of weights on a simply connected nilpotent Lie group G. Then for a subalgebra A of L¹(G) containing the Schwartz algebra 𝓢(G) as a dense subspace, we characterize all closed two-sided ideals of A whose hull reduces to one point which is a character.
4
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Spectral synthesis in L²(G)

81%
Ludwig J., Molitor-Braun C., Pusti S.
Colloquium Mathematicum
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2015
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tom 138
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nr 1
89-103
EN
For locally compact, second countable, type I groups G, we characterize all closed (two-sided) translation invariant subspaces of L²(G). We establish a similar result for K-biinvariant L²-functions (K a fixed maximal compact subgroup) in the context of semisimple Lie groups.
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