A Discrete Korovkin Theorem and BKW-Operators

✍ Scribed by Ryotaro Sato; Sin-Ei Takahasi

• Publisher: Elsevier Science
• Year: 1996
• Tongue: English
• Weight: 580 KB
• Volume: 84
• Category: Article
• ISSN: 0021-9045
• DOI: 10.1006/jath.1996.0023

✦ Synopsis

We give a functional Korovkin-type theorem on B(X ), the space of bounded complex-valued functions on an arbitrary set X and investigate a BKW-operator on B(X ) for a finite collection of test functions with a suitable property and a seminorm defined by a finite subset of X.

1996 Academic Press, Inc.

We first give a simple proof of the above theorem by considering the Stone-Cech compactification of Y endowed with the discrete topology.

Throughout all sections except for the last section, let X be a set and B(X ) the Banach space of bounded complex-valued functions on X with the supremum norm. Let E=[x 1 , ..., x m ]/X, f 0 =1, the identity of B(X ), and let [ f 1 , ..., f k ] be a finite collection of functions in B(X ) which satisfies the following two conditions: article no. 0023 351