Vol. 66, No. 1, 1976

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Conditions for simultaneous approximation and interpolation with norm preservation in C[a,b]

Joseph Michael Lambert

Vol. 66 (1976), No. 1, 173–180
Abstract

This paper gives necessary and sufficient conditions for a triple (X,M,Γ) to have property SAIN (simultaneous approximation and interpolation which preserves the norm), X being an arbitrary Banach space. The best previous result concerned X, a reflexive, rotund Banach space. The paper proceeds to use this result to yield geometric proofs of the work of D. J. Johnson concerning property SAIN and C[a,b].

Mathematical Subject Classification 2000
Primary: 41A65
Milestones
Received: 8 January 1976
Published: 1 September 1976
Authors
Joseph Michael Lambert