Approximate complementation and its applications in studying ideals of Banach algebras

Authors

  • Yong Zhang

DOI:

https://doi.org/10.7146/math.scand.a-14407

Abstract

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 (apα) (resp. (pαa)) converges to a uniformly for aK if and only if J is approximately complemented in the algebra.

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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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Articles