Cohen elements in Banach algebras
1979 ◽
Vol 84
(1-2)
◽
pp. 55-70
◽
Keyword(s):
SynopsisThe definition of Cohen elements in a commutative Banach algebra with a countable bounded approximate identity given by Esterle is modified slightly to be more analogous to the invertible elements in a unital Banach algebra. With the modified definition the n1-Cohen factorization results that were proved by Esterle are shown tohold in the semigroup of Cohen elements. If is the algebra of continuous complex valued functions vanishing at infinity on a σ-compact locally compact Hausdorff space X, then the Cohen elements in are identified and a natural quotient of a subsemigroup of Cohen elements is shown to be a group, isomorphic to the abstract index group of C(X∪{∞}).
2010 ◽
Vol 88
(3)
◽
pp. 289-300
◽
2000 ◽
Vol 23
(12)
◽
pp. 827-831
1978 ◽
Vol 30
(03)
◽
pp. 490-498
◽
1969 ◽
Vol 21
◽
pp. 751-754
◽
2018 ◽
Vol 11
(02)
◽
pp. 1850021
◽
1985 ◽
Vol 37
(4)
◽
pp. 664-681
◽
Keyword(s):
1978 ◽
Vol 21
(1)
◽
pp. 17-23
◽
Keyword(s):
1994 ◽
Vol 17
(4)
◽
pp. 671-680