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- Title
Core Theorems for Subsequences of Double Complex Sequences.
- Authors
Miller, Harry I.; Miller-Van Wieren, Leila
- Abstract
In this article we present core theorems for double sequences whose entries are complex numbers. These results extend work of Miller and Patterson [9] dealing with double sequences of real numbers. The proofs in this paper are much more involved then the proofs in the article just mentioned as the convex sets in the plane are, in general, much more involved then the trivial convex sets in the line. We give an answer to the following question. If w is a bounded double sequence with complex entries and A is a 4- dimensional matrix summability method, under what conditions on A does there exist z, a subsequence (rearrangement), of w such that each complex number t, in the core of w, is a limit point of Az?
- Subjects
MATHEMATICAL sequences; COMPLEX numbers; CONVEX sets; REARRANGEMENT invariant spaces; FUNCTION spaces
- Publication
Bulletin of the Belgian Mathematical Society - Simon Stevin, 2011, Vol 18, Issue 2, p345
- ISSN
1370-1444
- Publication type
Article
- DOI
10.36045/bbms/1307452084