Multidimensional Matrix Characterization of Asymptotic Equivalent and Ideal for Double Sequences
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.
Numerical Functional Analysis and Optimization
Digital Object Identifier (DOI)
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.