Vol. 34, No. 2, 1970

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ISSN: 0030-8730
On the existence question for a family of products

Gary Allen Gislason

Vol. 34 (1970), No. 2, 385–388
Abstract

Let X be a topological space and let P and Q be finite dimensional linear subspaces of C(X). Since the set PQ = {pq : p P,q Q} is a subset of a finite dimensional linear subspace of C(X), existence of best approximations from PQ is assured if and only if PQ is closed. If p P,q Q, and pq = 0 imply that p = 0 or q = 0, then PQ is shown to be closed. An example shows that PQ is not closed in general.

Mathematical Subject Classification
Primary: 41.60
Secondary: 46.00
Milestones
Received: 30 October 1969
Published: 1 August 1970
Authors
Gary Allen Gislason