Multidimensional Matrix Characterization of Asymptotic Equivalent and Ideal for Double Sequences
Document Type
Article
Publication Date
4-26-2019
Abstract
The goal of this article is to study I 2 equivalence double nonnegative sequences. To accomplish this we present a series of theorems that are similar to the following: If A is a nonnegative four dimensional summability matrix that maps bounded double sequences to l 2 and let I 2 and J 2 be admissible ideals in N × N then the following are equivalent. If X=X KI and Y=Y KI are bounded double sequences such that (Formula presented.) and (Formula presented.), for some d>0, then (Formula presented.) for each m and n, (Formula presented.) for each S 2 ϵ I 2 . In addition other variations and implications shall also be presented.
Publication Title
Numerical Functional Analysis and Optimization
Volume
40
Issue
6
First Page
654
Last Page
669
Digital Object Identifier (DOI)
10.1080/01630563.2018.1557204
ISSN
01630563
E-ISSN
15322467
Citation Information
Savas, R., Patterson, R.F. (2019) Multidimensional Matrix Characterization of Asymptotic Equivalent and Ideal for Double Sequences. Numerical Functional Analysis and Optimization, 40(6), 654-669.