Proximinality of subspaces and the quotient lifting property

Abstract

The Quotient Lifting Property (QLP) for pairs of spaces and its relation to the proximinality of subspaces are studied. Even though this property is not hereditary, for finite-dimensional subspaces of (Formula presented.), we show that for a choice of a basis, all subspaces spanned by any sub-collection from the base, generate subspaces with QLP. Spaces of dimension greater than two with the total quotient lifting property are shown to be Hilbert spaces.

Publication Title

Linear and Multilinear Algebra

Link to Full Text

Share

COinS