Abstract
Compact linear operators have a key role in functional analysis and operator theory, with a particularly important place in the study of boundary-value problems for elliptic differential equations. They have properties which are reminiscent of linear operators acting in finite-dimensional spaces, and Theorem 1.2.25 shows a Banach space Y has the approximation property (AP) if and only if given any Banach space X and any compact map T ∈ B (X, Y), T can be approximated arbitrarily closely in norm by a finite rank operator.
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© 2013 Springer Basel
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Edmunds, D.E., Evans, W.D. (2013). Representation of Compact Linear Operators. In: Representations of Linear Operators Between Banach Spaces. Operator Theory: Advances and Applications, vol 238. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-0642-8_2
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DOI: https://doi.org/10.1007/978-3-0348-0642-8_2
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Publisher Name: Birkhäuser, Basel
Print ISBN: 978-3-0348-0641-1
Online ISBN: 978-3-0348-0642-8
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