Hensgen, Wolfgang (1996) Extremal problems for the vector-valued (L(1)/H-0(1), H-infinity) duality. JOURNAL OF APPROXIMATION THEORY, 84 (2). pp. 162-171. ISSN 0021-9045
Full text not available from this repository.Abstract
Let X be a complex Banach space and L(1)(X):=L(1)(T; X) the Bochner space on the circle T. The X-valued Hardy space H-0(1)(X):={f is an element of L(1)(X):(f) over cap(n)=0 For All n equal to or less than 0} is proximinal in L(1)(X) if H has ARNP and is contractively complemented in X''. It is semi-Chebyshev if X is strictly convex. With H-infinity(X') the dual space of L(1)(X)/H-0(1)(X), extremal kernels and functions for this duality are studied. Proximinality fails for X:=L(1)/H-0(1); this is equivalent to the assertion that for Lambda:=N x Z boolean OR Z x N, L(Lambda)(1)(T-2) is not proximinal in L(1)(T-2). A class of subsets Lambda subset of Z(2) is described for which this non-proximinality holds. (C) 1996 Academic Press, Inc.
| Item Type: | Article |
|---|---|
| Subjects: | 500 Science > 510 Mathematics |
| Divisions: | Mathematics |
| Depositing User: | Dr. Gernot Deinzer |
| Date Deposited: | 14 Nov 2023 08:44 |
| Last Modified: | 14 Nov 2023 08:44 |
| URI: | https://pred.uni-regensburg.de/id/eprint/51963 |
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