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Consistent classes of double summability methods

✍ Scribed by Richard F. Patterson; Ekrem Savaş

Publisher
Elsevier Science
Year
2010
Tongue
English
Weight
237 KB
Volume
23
Category
Article
ISSN
0893-9659

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✦ Synopsis

In 2000 Patterson proved that if a bounded double sequence is divergent then there are RHregular matrix methods that sum it to various values. It is now natural to ask the following question. Is there a collection Υ of RH-regular matrix methods which are consistent and such that every bounded double sequence is summable by at least one method in the collection? Similar to Goffman and Petersen's presentation we will present a class of such a collection. In addition, it is clear from the presentation here that it is extremely difficult to find all such collections. However, we have extended this class to a countable collection of RH-regular matrix methods with bounded norm.

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