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A note on generalized projections in c₀

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Deręgowska B., Lewandowska B.

Annales Polonici Mathematici

2014

tom 111

nr 1

59-72

Let V ⊂ Z be two subspaces of a Banach space X. We define the set of generalized projections by $𝓟_V(X,Z):= {P ∈ 𝓛(X,Z): P|_V = id}$. Now let X = c₀ or $l^m_∞$, Z:= kerf for some f ∈ X* and $V:= Z ∩ lⁿ_∞$ (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.

Ograniczanie wyników

1 Annales Polonici Mathematici

1 Deręgowska B.

1 Lewandowska B.

1 2014

Wyniki wyszukiwania

A note on generalized projections in c₀