The Second Dual of the Group Algebra of a Compact Group

Işık, Nilgün; Pym, J. S.; Ülger, A.

doi:10.1112/jlms/s2-35.1.135

Cited by 48 publications

(35 citation statements)

References 3 publications

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“…In [5], Grosser-Losert showed that Z t (LU C(G) * ) = M (G) if G is abelian, where M (G) is the measure algebra of G. Lau [15] extended this result to all locally compact groups. For the group algebra L 1 (G), Isik-Pym-Ülger [12] …”

Section: Where Lu C(g) Is the Space Of Bounded Left Uniformly Continumentioning

confidence: 99%

Open subgroups and the centre problem for the Fourier algebra

2006

Proc. Amer. Math. Soc.

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Let A ( G ) A(G) be the Fourier algebra of a locally compact group and U C B ( G ^ ) UCB(\hat {G}) the C ∗ C^* -algebra of uniformly continuous linear functionals on A ( G ) A(G) . We study how the centre problem for the algebra U C B ( G ^ ) ∗ UCB(\hat {G})^* (resp. A ( G ) ∗ ∗ A(G)^{**} ) is related to the centre problem for the algebras U C B ( H ^ ) ∗ UCB(\hat {H})^* (resp. A ( H ) ∗ ∗ A(H)^{**} ) of σ \sigma -compact open subgroups H H of G G . We extend some results of Lau-Losert on the centres of U C B ( G ^ ) ∗ UCB(\hat {G})^* and A ( G ) ∗ ∗ A(G)^{**} .

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Section: Where Lu C(g) Is the Space Of Bounded Left Uniformly Continumentioning

confidence: 99%

Open subgroups and the centre problem for the Fourier algebra

2006

Proc. Amer. Math. Soc.

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“…In [25] Parsons proved that, for certain abelian discrete groups G, for the algebra A = 1 (G), Z 1 = A. In [18] Isik, Pym andÜlger showed that, for any compact group G, the topological center of L 1 (G) * * is L 1 (G). This result has been extended to all locally compact groups by Lau and Losert in [21].…”

Section: Introductionmentioning

confidence: 99%

Topological centers of certain dual algebras

Lau

Ülger²

1996

Trans. Amer. Math. Soc.

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Abstract. Let A be a Banach algebra with a bounded approximate identity. Let Z 1 and Z 2 be, respectively, the topological centers of the algebras A * * and (A * A) * . In this paper, for weakly sequentially complete Banach algebras, in particular for the group and Fourier algebras L 1 (G) and A(G), we study the sets Z 1 , Z 2 , the relations between them and with several other subspaces of A * * or A * .

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“…For a locally compact group, they proved most of the results obtained in [4] for L ∞ 0 (G) * . In fact, they introduced a sensible replacement for L ∞ (G), when G is compact.…”

Section: Introductionmentioning

confidence: 61%

“…Isik and et al [4] gave some interesting results on the structure of the Banach algebra L ∞ (G) * , for an infinite compact group G. Lau and Pym [8] introduced the subspace…”

Section: Introductionmentioning

confidence: 99%

Derivations on Convolution Algebras

J.¹,

Saeedi²

2015

Bulletin of the Korean Mathematical Society

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Abstract. In this paper, we investigate derivations on the noncommutative Banach algebra L ∞ 0 (ω) * equipped with an Arens product. As a main result, we prove the Singer-Wermer conjecture for the noncommutative Banach algebra L ∞ 0 (ω) * . We then show that a derivation on L ∞ 0 (ω) * is continuous if and only if its restriction to rad(L ∞ 0 (ω) * ) is continuous. We also prove that there is no nonzero centralizing derivation on L ∞ 0 (ω) * . Finally, we prove that the space of all inner derivations of L ∞ 0 (ω) * is continuously homomorphic to the space L ∞ 0 (ω) * /L 1 (ω).

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The Second Dual of the Group Algebra of a Compact Group

Cited by 48 publications

References 3 publications

Open subgroups and the centre problem for the Fourier algebra

Open subgroups and the centre problem for the Fourier algebra

Topological centers of certain dual algebras

Derivations on Convolution Algebras

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