On amenability of the Banach algebras l∞(S, [Ufr ])
2002 ◽
Vol 132
(2)
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pp. 319-322
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Let [Ufr ] be an associative Banach algebra. Given a set S, we write l∞(S, [Ufr ]) for the Banach algebra of all bounded functions f: S→[Ufr ] with the usual norm ∥f∥∞ = sups∈S∥f(s)∥[Ufr ] and pointwise multiplication. When S is countable, we simply write l∈([Ufr ]).In this short note, we exhibit examples of amenable (resp. weakly amenable) Banach algebras [Ufr ] for which l∈(S, [Ufr ]) fails to be amenable (resp. weakly amenable), thus solving a problem raised by Gourdeau in [7] and [8]. We refer the reader to [4, 9, 10] for background on amenability and weak amenability. For basic information about the Arens product in the second dual of a Banach algebra the reader can consult [5, 6].
2002 ◽
Vol 65
(2)
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pp. 191-197
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2001 ◽
Vol 44
(4)
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pp. 504-508
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1992 ◽
Vol 111
(1)
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pp. 161-168
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2008 ◽
Vol 45
(1)
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pp. 1-11
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1989 ◽
Vol 105
(2)
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pp. 351-355
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1975 ◽
Vol 27
(5)
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pp. 1029-1035
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2008 ◽
Vol 50
(3)
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pp. 539-555
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