A note on generalized projections in c₀

Beata Deręgowska, and Barbara Lewandowska. "A note on generalized projections in c₀." Annales Polonici Mathematici 111.1 (2014): 59-72. <http://eudml.org/doc/280500>.

@article{BeataDeręgowska2014,
abstract = {Let V ⊂ Z be two subspaces of a Banach space X. We define the set of generalized projections by $_V(X,Z):= \{P ∈ (X,Z): P|_V = id\}$. 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.},
author = {Beata Deręgowska, Barbara Lewandowska},
journal = {Annales Polonici Mathematici},
keywords = {minimal projection; minimal generalized projection; strong uniqueness},
language = {eng},
number = {1},
pages = {59-72},
title = {A note on generalized projections in c₀},
url = {http://eudml.org/doc/280500},
volume = {111},
year = {2014},
}

TY - JOUR
AU - Beata Deręgowska
AU - Barbara Lewandowska
TI - A note on generalized projections in c₀
JO - Annales Polonici Mathematici
PY - 2014
VL - 111
IS - 1
SP - 59
EP - 72
AB - Let V ⊂ Z be two subspaces of a Banach space X. We define the set of generalized projections by $_V(X,Z):= {P ∈ (X,Z): P|_V = id}$. 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.
LA - eng
KW - minimal projection; minimal generalized projection; strong uniqueness
UR - http://eudml.org/doc/280500
ER -