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 , 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.
2000 Mathematics Subject Classifications:
Acknowledgments
The authors are grateful to the referee for a careful reading and many useful suggestions.
Disclosure statement
No potential conflict of interest was reported by the author(s).