Complemented Banach Algebras
Keyword(s):
Let A be a complex Banach algebra and Lr (Ll) be the lattice of all closed right (left) ideals in A. Following Tomiuk (5), we say that A is a right complemented algebra if there exists a mapping I —> IP of Lτ into Lr such that if I ∊ Lr, then I ∩ Ip = (0), (Ip)p = I, I ⴲ Ip = A and if I1, I2 ∊ Lr with I1 ⊆ I2 then .If in a Banach algebra A every proper closed right ideal has a non-zero left annihilator, then A is called a left annihilator algebra. If, in addition, the corresponding statement holds for every proper closed left ideal and r(A) = (0) = l(A), A is called an annihilator algebra (1).
1978 ◽
Vol 21
(1)
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pp. 81-85
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1993 ◽
Vol 47
(3)
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pp. 505-519
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2001 ◽
Vol 44
(4)
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pp. 504-508
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1973 ◽
Vol 14
(2)
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pp. 128-135
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1979 ◽
Vol 20
(2)
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pp. 247-252
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1979 ◽
Vol 86
(2)
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pp. 271-278
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Keyword(s):
Keyword(s):
1973 ◽
Vol 18
(4)
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pp. 295-298
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Keyword(s):
Keyword(s):
1979 ◽
Vol 20
(2)
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pp. 211-215
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