Matrix maps of bounded sequences in a Banach space

Author:

Maddox I. J.

Abstract

Matrices of bounded linear operators are applied to bounded sequences in a Banach space. The main result is related to Knopp’s core theorem for scalar sequences and matrices. From the main result, necessary and sufficient conditions are given for a matrix of operators to map bounded sequences into null sequences in a Banach space.

Publisher

American Mathematical Society (AMS)

Subject

Applied Mathematics,General Mathematics

Reference4 articles.

1. Effects of linear transformations on the divergence of bounded sequences and functions;Lev, Joseph;Trans. Amer. Math. Soc.,1933

2. Unbounded operators and a theorem of A. Robinson;Lorentz, G. G.;Trans. Roy. Soc. Canada Sect. III,1952

3. On functional transformations and summability;Robinson, A.;Proc. London Math. Soc. (2),1950

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