Sequences of bounded summability domains

Robert M. DeVos and Frederick W. Hartmann

Vol. 74 (1978), No. 2, 333–338

DOI: 10.2140/pjm.1978.74.333

Abstract

C. Goffman and G. N. Wollan conjectured that the bounded summability field of a regular matrix A is so thin that the union of countably many such sets is not dense in m. G. M. Petersen proved this conjecture. This result is strengthened by showing if A is a noncoercive matrix whose summability field contains all the finite sequences then its bounded summability field is so thin that the union of countably many such sets is not dense in m. An example is given to show that the condition of containing the finite sequences is necessary.

Mathematical Subject Classification 2000

Primary: 40D20

Secondary: 40H05

Milestones

Received: 4 April 1977

Revised: 8 August 1977

Published: 1 February 1978