Displaying similar documents to “Best simultaneous L p approximations”

The dual form of the approximation property for a Banach space and a subspace

T. Figiel, W. B. Johnson (2015)

Studia Mathematica

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Given a Banach space X and a subspace Y, the pair (X,Y) is said to have the approximation property (AP) provided there is a net of finite rank bounded linear operators on X all of which leave the subspace Y invariant such that the net converges uniformly on compact subsets of X to the identity operator. In particular, if the pair (X,Y) has the AP then X, Y, and the quotient space X/Y have the classical Grothendieck AP. The main result is an easy to apply dual formulation of this property....

Strong unicity criterion in some space of operators

Grzegorz Lewicki (1993)

Commentationes Mathematicae Universitatis Carolinae

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Let X be a finite dimensional Banach space and let Y ⊂ X be a hyperplane. Let L Y = { L ∈ L ( X , Y ) : L ∣ Y = 0 } . In this note, we present sufficient and necessary conditions on L 0 ∈ L Y being a strongly unique best approximation for given L ∈ L ( X ) . Next we apply this characterization to the case of X = l ∞ n and to generalization of Theorem I.1.3 from [12] (see also [13]).