Wyniki wyszukiwania

1

Fell's subgroup algebra for locally compact abelian groups and $L^1$-covariance algebras

100%

Poguntke D.

Colloquium Mathematicum

|

1996

|

tom 69

|

nr 2

239-265

2

An example of a generalized completely continuous representation of a locally compact group

100%

Poguntke D.

Studia Mathematica

|

1993

|

tom 105

|

nr 2

189-205

EN

There is constructed a compactly generated, separable, locally compact group G and a continuous irreducible unitary representation π of G such that the image π(C*(G)) of the group C*-algebra contains the algebra of compact operators, while the image $π(L^1(G))$ of the $L^1$-group algebra does not containany nonzero compact operator. The group G is a semidirect product of a metabelian discrete group and a "generalized Heisenberg group".

3

Banach algebras associated with Laplacians on solvable Lie groups and injectivity of the Harish-Chandra transform

100%

Poguntke D.

Colloquium Mathematicum

|

2010

|

tom 118

|

nr 1

283-298

EN

For any connected Lie group G and any Laplacian Λ = X²₁ + ⋯ + X²ₙ ∈ 𝔘𝔤 (X₁,...,Xₙ being a basis of 𝔤) one can define the commutant 𝔅 = 𝔅(Λ) of Λ in the convolution algebra ℒ¹(G) as well as the commutant ℭ(Λ) in the group C*-algebra C*(G). Both are involutive Banach algebras. We study these algebras in the case of a "distinguished Laplacian" on the "Iwasawa part AN" of a semisimple Lie group. One obtains a fairly good description of these algebras by objects derived from the semisimple group. As a consequence one sees that both algebras are commutative (which is not immediate from the definition), 𝔅 is C*-dense in ℭ, and 𝔅 is a completely regular symmetric Wiener algebra. As a byproduct of our approach we give another proof of the injectivity of Harish-Chandra's spherical Fourier transform, which is based on a theorem on C*-algebras of solvable Lie groups (due to N. V. Pedersen). The article closes with some open questions for more general solvable Lie groups. To some extent the article is written with a view to these questions, that is, we try to apply, as much as possible (at the moment), methods which work also outside the semisimple context.

4

Discrete nilpotent groups have a $T_{1}$ primitive ideal space

32%

Poguntke D.

Studia Mathematica

|

1981-1982

|

tom 71

|

nr 3

271-275

Ograniczanie wyników

2 Colloquium Mathematicum

2 Studia Mathematica

4 Poguntke D.

1 2010

1 1996

1 1993

1 1982

Fell's subgroup algebra for locally compact abelian groups and $L^1$-covariance algebras

An example of a generalized completely continuous representation of a locally compact group

Banach algebras associated with Laplacians on solvable Lie groups and injectivity of the Harish-Chandra transform

Discrete nilpotent groups have a $T_{1}$ primitive ideal space