Maximal one-sided ideals in Banach algebras
1976 ◽
Vol 80
(1)
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pp. 109-111
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In (1) Akemann and Rosenfeld introduced a property for Banach algebras which they called (*). A Banach algebra satisfies (*) if every maximal one-sided ideal in is closed. They proved that certain classes of Banach algebra with satisfy (*), and they mentioned a conjecture that if is a Banach algebra with , then satisfies (*). In this paper we show that, if is a Banach algebra with a bounded right (left) approximate identity, then maximal left (right) ideals in are closed, and we give a counter-example to the above conjecture. We also give an independent proof that C*-algebras satisfy (*).
1989 ◽
Vol 105
(2)
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pp. 351-355
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2001 ◽
Vol 44
(4)
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pp. 504-508
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Keyword(s):
1986 ◽
Vol 28
(2)
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pp. 211-214
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1990 ◽
Vol 107
(3)
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pp. 557-571
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Keyword(s):
Keyword(s):
1992 ◽
Vol 111
(1)
◽
pp. 161-168
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Keyword(s):
1979 ◽
Vol 86
(2)
◽
pp. 271-278
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Keyword(s):
1981 ◽
Vol 23
(2)
◽
pp. 265-281
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