On an extension of the Stone–Weierstrass theorem

Kuppum V. Srikanth; Raj Bhawan Yadav

Vol. 19 No. 2 (2014)

Regular Articles

On an extension of the Stone–Weierstrass theorem

Published 2014-10-15

Kuppum V. Srikanth
Raj Bhawan Yadav

Kuppum V. Srikanth
Dept. of Mathematics, Indian Institute of Technology Guwahati Assam 781 039 INDIA

Raj Bhawan Yadav
Dept. of Mathematics Indian Institute of Technology Guwahati Assam 781 039 INDIA

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Abstract

The classical Stone-Weierstrass Theorem has been generalized and extended in different directions. Theorem 1 of [2] (D. Hill, E. Passow, and L. Raymon, Approximation with interpolatory constraints, Illinois J. Math. Volume 20, Issue 1 (1976), 65-71) may be viewed as one such extension involving finitely many interpolatory constraints. This article generalizes the latter theorem to the case where the constraints are on an arbitrary closed subset of the compact metric space under consideration. We also present an alternative proof of the cited Theorem.

Keywords

Stone-Weierstrass, interpolation, dense subset, metric space

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Author Biography

Kuppum V. Srikanth

Mathematics and Assistant Professor

Raj Bhawan Yadav

Mathematics Department and Graduate Student (Ph.D.)