Harmonic analysis and centers of group algebras

Liukkonen, John R.; Mosak, Richard D.

doi:10.1090/s0002-9947-1974-0350322-7

Cited by 42 publications

(25 citation statements)

References 17 publications

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“…mutative Banach algebra with continuous symmetric involution and bounded approximate identity [15]. In this paper we investigate the problem of existence of finite universal Korovkin sets for the algebra…”

Section: Z(li(g)) Of La(g) Is Nontrivial Iff G Has a Compact Invarianmentioning

confidence: 99%

On existence of finite universal Korovkin sets in the centre of group algebras

Agrawal

Tewari

1997

Monatshefte f�r Mathematik

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Abstract.In this paper, we characterize compact groups G as well as connected central topological groups G for which the centre Z(LI(G)) admits a finite universal Korovkin set. Also we prove that if G is a non-connected central topological group which has a compact open normal subgroup K such that G = KZ, then Z(LI(G)) admits a finite universal Korovkin set if is a finite-dimensional separable metric space or equivalently G is separable metrizable and G/K has finite torsion-free rank.

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Section: Z(li(g)) Of La(g) Is Nontrivial Iff G Has a Compact Invarianmentioning

confidence: 99%

On existence of finite universal Korovkin sets in the centre of group algebras

Agrawal

Tewari

1997

Monatshefte f�r Mathematik

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“…There is an obvious relation between 2?-invariant measures or functions on G and measures or functions on G B . We note that G B may be identified with the set of all continuous nonzero positive definite ^-invariant functions φ on G which satisfy φ(x)φ(y) = f B φ(xβ(y)) dβ, where dβ is the normalized Haar measure on B, see [16] and [17]. In [9] it is shown that G B is a hypergroup with respect to pointwise multiplication.…”

Section: Definite Further μ Is Also the Levy Measure Of (V T ) Wherementioning

confidence: 99%

Convolution semigroups on hypergroups

Lasser¹

1987

Pacific J. Math.

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Dedicated to Professor Elmar Thoma on the occasion of his 60 th birthdayThe purpose of this paper is to establish a unified treatment of many disparate theorems of Levy-Hinέin type. The appropriate framework to do this is the theory of commutative hypergroups. In this way we not only generalize the results mentioned above but also settle some asymmetries indicated above. Roughly speaking a hypergroup K is a space in which the product of two elements is a probability measure on this space satisfying certain conditions. If K is commutative and if the space K of characters is a hypergroup under pointwise operations a Levy-Hincin formula for convolution semigroups is obtained. Before setting up some notation we show how the examples fit in.

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“…Man iiberlegt sieh schnell, dab L 1 (G) eine approxima~ive Eins aus JB (oo) c~ Z~ (G) besitzt. In [13] …”

Section: Ftir # E3b (G) Definierg Fi (E)= Fz (X)d# (X) Eine Stetige Funclassified

Zur Idealtheorie in Gruppenalgebren von [FIA] B ? -Gruppen

Lasser¹

1978

Monatshefte f�r Mathematik

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On Ideals in Group Algebras of [FIA]B-Groups. In this paper we consider closed B-invariant ideals in the group algebra LI(G), where G is a locally compact group with a relatively compact group B of topological automorphisms, which contains the set of all inner automorphisms. We study conditions when closed B-invariant ideals are completely determined by their hull. Also questions concerning the existence of approximate units in these ideals will be answered. Above all, we shall study these properties with regard to the relations between ideals in LI(G), LI(G/N) and LI(N), where N is a closed Bdnvariant subgroup of G.

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Harmonic analysis and centers of group algebras

Cited by 42 publications

References 17 publications

On existence of finite universal Korovkin sets in the centre of group algebras

On existence of finite universal Korovkin sets in the centre of group algebras

Convolution semigroups on hypergroups

Zur Idealtheorie in Gruppenalgebren von [FIA] B ? -Gruppen

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