✦ LIBER ✦
Extremal Problems for the Vector-Valued 〈L1/H01, H∞〉 Duality
✍ Scribed by Wolfgang Hensgen
- Publisher
- Elsevier Science
- Year
- 1996
- Tongue
- English
- Weight
- 473 KB
- Volume
- 84
- Category
- Article
- ISSN
- 0021-9045
No coin nor oath required. For personal study only.
✦ Synopsis
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
, extremal kernels and functions for this duality are studied. Proximinality fails for X :=L 1 ÂH 1 0 ; this is equivalent to the assertion that for 4 := N_Z _ Z_N, L 1 4 (T 2 ) is not proximinal in L 1 (T 2 ). A class of subsets 4/Z 2 is described for which this non-proximinality holds.