Galois-Tuckey Equivalence of Convergent Series and Matrix Summability
by
Winfried Just
Ohio University
Coauthors: Peter Vojtás (Slovak Academy of Sciences)

Let us denote by M the set of all regular matrices A={ a_{i, j} } with nonnegative entries and such that the limit of suprema of rows tends to 0 (to ensure the support of this matrix is a nowhere dense subset of \omega^*). For X subset or equal \omega let c_X denote the characteristic function of X. We define a binary relation RLIM subset or equal M×[\omega]^\omega as follows: (A, X) in RLIM iff lim_{i --> \infty}\sum_j=0^\inftya_{i, j}c_X(j)=0. Moreover, we define a binary relation CONV subset or equal (c₀\l¹)×[\omega]^\omega by: (a, X) in CONV iff \sum_{n in X}a_n < +\infty.

We show that the relations CONV and RLIM are Galois-Tukey equivalent and derive some consequences from this fact.

Date received: April 12, 1996

Copyright © 1996 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # caae-44.