Central Approximate Units in a Certain Ideal of L 1 (G)

Kotzmann, Ernst; Rindler, Harald

doi:10.2307/2040886

Cited by 3 publications

(6 citation statements)

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“…Mosak, [7], proved that LX(G) satisfies (Ac) iff G E [SIN]. Reiter,[9], proved that L°(G) satisfies (A) iff G is amenable and Kotzmann, Rindler, [5], that…”

Section: M°(g) = ¡M G M(g) F 1 Dm = O} L°(g) = M°(g) N Ex(g)mentioning

confidence: 99%

“…The proof of 7 is contained in [7], that of 9 in [5]. ([11], for a proof see [6]) there exists a compact normal subgroup K such that G/K = V X D, V a vector group, D a discrete [FC]-group.…”

Section: M°(g) = ¡M G M(g) F 1 Dm = O} L°(g) = M°(g) N Ex(g)mentioning

confidence: 99%

“…Several properties of locally compact groups can be characterized by the existence of certain approximate units in 3 ideals of the group algebra. We combine methods and results from [8], [7], [5]. …”

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confidence: 99%

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Approximate units in ideals of group algebras

Rindler¹

1978

Proc. Amer. Math. Soc.

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“…Mosak, [7], proved that LX(G) satisfies (Ac) iff G E [SIN]. Reiter,[9], proved that L°(G) satisfies (A) iff G is amenable and Kotzmann, Rindler, [5], that…”

Section: M°(g) = ¡M G M(g) F 1 Dm = O} L°(g) = M°(g) N Ex(g)mentioning

confidence: 99%

Section: M°(g) = ¡M G M(g) F 1 Dm = O} L°(g) = M°(g) N Ex(g)mentioning

confidence: 99%

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Approximate units in ideals of group algebras

Rindler¹

1978

Proc. Amer. Math. Soc.

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“…It follows from [11,Theorem 3] that we can approximate u by functions of the form w = 2*_i/" ® Xn> where /" £ LX(V) with/, E K(V), 1 < n < N, and x", 1< n < N, are characters of K (see [7,Chapter 5,§4.1(1)] and [10, p. 85] here Saw(x) = w(ax), a E B". Since B~ is compact and the Fourier transform of w has compact support, we have w# = 2^_i gOT®Xm> where gm £ L\V) with gm E K(V).…”

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confidence: 99%

Segal algebras on non-abelian groups

Kotzmann¹,

Rindler²

1978

Trans. Amer. Math. Soc.

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Abstract. Let Sl(G) be a Segal algebra on a locally compact group. The central functions of S '(G) are dense in the center of L\G). S\G) has central approximate units iff G G [SIN]. This is a generalization of a result of Reiter on the one hand and of Mosak on the other hand. The proofs depend on the structure theorems of [S/JV]-and [W]-groups. In the second part some new examples of Segal algebras are constructed. A locally compact group is discrete or Abelian iff every Segal algebra is rightinvariant. As opposed to the results, the proofs are not quite obvious.

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“…Mosak, [7], proved that LX(G) satisfies (Ac) iff G E [SIN]. Reiter,[9], proved that L°(G) satisfies (A) iff G is amenable and Kotzmann, Rindler, [5], that L°(G) satisfies (Ac) iff G G [FIA]-.…”

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confidence: 99%