Finite dimensionality, nilpotents and quasinilpotents in Banach algebras
1974 ◽
Vol 19
(1)
◽
pp. 45-49
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Keyword(s):
In this note we present some rather loosely connected results on Banach algebras together with some illustrative examples. We consider various conditions on a Banach algebra which imply that it is finite dimensional. We also consider conditions which imply the existence of non-zero nilpotents, and hence the existence of finite dimensional subalgebras. In the setting of Banach algebras quasinilpotents figure more prominently than nilpotents. We give an example of a non-commutative Banach algebra in which 0 is the only quasinilpotent; this resolves a problem of Hirschfeld and Zelazko (4).
1984 ◽
Vol 7
(3)
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pp. 519-522
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Keyword(s):
1976 ◽
Vol 20
(1)
◽
pp. 1-5
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Keyword(s):
2018 ◽
Vol 11
(02)
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pp. 1850021
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1959 ◽
Vol 11
◽
pp. 297-310
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2001 ◽
Vol 6
(1)
◽
pp. 138-146
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2006 ◽
Vol 81
(2)
◽
pp. 279-296
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Keyword(s):
1989 ◽
Vol 105
(2)
◽
pp. 351-355
◽
Keyword(s):
2020 ◽
Vol 57
(3)
◽
pp. 290-297