The Second Conjugates of Certain Banach Algebras
1975 ◽
Vol 27
(5)
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pp. 1029-1035
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Keyword(s):
Let A be a Banach algebra and A** its second conjugate space. Arens has denned two natural extensions of the product on A to A**. Under either Arens product, A** becomes a Banach algebra. Let A be a semisimple Banach algebra which is a dense two-sided ideal of a B*-algebra B and R** the radical of (A**, o). We show that A** = Q ⊕ R**, where Q is a closed two-sided ideal of A**, o). This was inspired by Alexander's recent result for simple dual A*-algebras (see [1, p. 573, Theorem 5]). We also obtain that if A is commutative, then A is Arens regular.
2002 ◽
Vol 65
(2)
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pp. 191-197
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Keyword(s):
1996 ◽
Vol 120
(3)
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pp. 455-473
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Keyword(s):
2002 ◽
Vol 132
(2)
◽
pp. 319-322
Keyword(s):
2008 ◽
Vol 50
(3)
◽
pp. 539-555
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Keyword(s):
1988 ◽
Vol 38
(1)
◽
pp. 77-81
1998 ◽
Vol 41
(3)
◽
pp. 625-630
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Keyword(s):
1992 ◽
Vol 111
(1)
◽
pp. 161-168
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Keyword(s):
1984 ◽
Vol 7
(3)
◽
pp. 519-522
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Keyword(s):