A note on generalized projections in c₀

• Autorzy: Beata Deręgowska , Barbara Lewandowska
• Języki publikacji: EN

Abstrakty

EN

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.

Kategorie tematyczne

• 47A58: Operator approximation theory
• 41A52: Uniqueness of best approximation

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Annales Polonici Mathematici
• Rocznik: 2014
• Tom: 111
• Numer: 1
• Strony: 59-72

Daty

wydano

2014

Twórcy

autor

Beata Deręgowska

• Faculty of Mathematics and Computer Science, Jagiellonian University, Łojasiewicza 6, 30-048 Kraków, Poland

autor

Barbara Lewandowska

• Faculty of Mathematics and Computer Science, Jagiellonian University, Łojasiewicza 6, 30-048 Kraków, Poland

Identyfikatory

DOI

10.4064/ap111-1-5