A note on generalized projections in c₀

Beata Deręgowska; Barbara Lewandowska

Annales Polonici Mathematici, Tome 111 (2014), p. 59-72 / Harvested from The Polish Digital Mathematics Library

Résumé

Let V ⊂ Z be two subspaces of a Banach space X. We define the set of generalized projections by $_{V} (X, Z) : = {P \in (X, Z) : P |}_{V} = i d$ . Now let X = c₀ or $l_{\infty}^{m}$ , Z:= kerf for some f ∈ X* and $V : = Z \cap l ⁿ_{\infty}$ (n < m). The main goal of this paper is to discuss existence, uniqueness and strong uniqueness of a minimal generalized projection in this case. Also formulas for the relative generalized projection constant and the strong uniqueness constant will be given (cf. J. Blatter and E. W. Cheney [Ann. Mat. Pura Appl. 101 (1974), 215-227] and G. Lewicki and A. Micek [J. Approx. Theory 162 (2010), 2278-2289] where the case of projections has been considered). We discuss both the real and complex cases.

Publié le : 2014-01-01

Zbl 1311.47015

EUDML-ID : urn:eudml:doc:280500

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     title = {A note on generalized projections in c0},
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Beata Deręgowska; Barbara Lewandowska. A note on generalized projections in c₀. Annales Polonici Mathematici, Tome 111 (2014) pp. 59-72. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-ap111-1-5/