Edmunds, D. E., Evans, William Desmond and Harris, D. J. 2013. The structure of compact linear operators in Banach spaces. Revista Mathematica Complutense 26 (2) , pp. 445-469. 10.1007/s13163-012-0107-x |
Abstract
In Edmunds et al. [J Lond Math Soc 78(2):65–84, 2008], a representation of a compact linear operator T acting between reflexive Banach spaces X and Y with strictly convex duals was established in terms of elements xn∈X, projections Pn of X onto subspaces Xn which are such that ∩Xn=kerT, and linear projections Sn satisfying Snx=∑n−1j=1ξj(x)xj, where the coefficients ξj(x) are given explicitly. If kerT={0} and the condition (A):sup∥Sn∥<∞ is satisfied, the representation reduces to an analogue of the Schmidt representation of T when X and Y are Hilbert spaces, and also (xn) is a Schauder basis of X; thus condition (A) can not be satisfied if X does not have the approximation property. In this paper we investigate circumstances in which (A) does or does not hold, and analyse the implications.
Item Type: | Article |
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Status: | Published |
Schools: | Mathematics |
Subjects: | Q Science > QA Mathematics |
Publisher: | Springer |
Last Modified: | 04 Jun 2017 08:57 |
URI: | http://orca.cf.ac.uk/id/eprint/88266 |
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