Approximate complementation and its applications in studying ideals of Banach algebras
DOI:
https://doi.org/10.7146/math.scand.a-14407Abstract
We show that a subspace of a Banach space having the approximation property inherits this property if and only if it is approximately complemented in the space. For an amenable Banach algebra a closed left, right or two-sided ideal admits a bounded right, left or two-sided approximate identity if and only if it is bounded approximately complemented in the algebra. If an amenable Banach algebra has a symmetric diagonal, then a closed left (right) ideal J has a right (resp. left) approximate identity (pα) such that, for every compact subset K of J, the net (a⋅pα) (resp. (pα⋅a)) converges to a uniformly for a∈K if and only if J is approximately complemented in the algebra.Downloads
Published
2003-06-01
How to Cite
Zhang, Y. (2003). Approximate complementation and its applications in studying ideals of Banach algebras. MATHEMATICA SCANDINAVICA, 92(2), 301–308. https://doi.org/10.7146/math.scand.a-14407
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