Some Summability Invariants
Journal
Manuscripta Mathematica
Journal Volume
31
Journal Issue
4
Pages
363-378
Date Issued
1980
Author(s)
Beekmann, W.
Abstract
For summability matrices A, Macphail has introduced a condition (E′): for sequences t∈ℓ and x in the summability field of A we have t(Ax)=(tA) x, whenever (tA) x exists. He showed that, if the A-limit is the nullfunctional, the condition (E′) is equivalent to the invariance of the equation {Mathematical expression}. We prove that the condition (E′) invariance of the equation {Mathematical expression} also in the more general case of non-μ-unique matrices. Moreover, we give some partial solutions to the open question in [3] whether the invariance of {Mathematical expression} implies that of I. © 1980 Springer-Verlag.
Type
journal article