Commutativity of Banach algebras characterized by primitive ideals and spectra
Keyword(s):
This study is an attempt to prove the following main results. Let A be a Banach algebra and U = A ? C be its unitization. By ?c(U), we denote the set of all primitive ideals P of U such that the quotient algebra U/P is commutative. We prove that if A is semi-prime and dim(?P??c(U)P)? 1, then A is commutative. Moreover, we prove the following: Let A be a semi-simple Banach algebra. Then, A is commutative if and only if G(a) = {?(a)? ? ?A} ? {0} or G(a) = {?(a)| ? ? ?A} for every a ? A, where G(a) and ?A denote the spectrum of an element a ? A, and the set of all non-zero multiplicative linear functionals on A, respectively.
1981 ◽
Vol 24
(1)
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pp. 31-40
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1983 ◽
Vol 27
(1)
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pp. 115-119
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2018 ◽
Vol 11
(02)
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pp. 1850021
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1967 ◽
Vol 8
(1)
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pp. 41-49
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2018 ◽
Vol 17
(09)
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pp. 1850169
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1959 ◽
Vol 11
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pp. 297-310
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2001 ◽
Vol 6
(1)
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pp. 138-146
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1988 ◽
Vol 44
(2)
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pp. 143-145
1985 ◽
Vol 37
(4)
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pp. 664-681
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