Abstract
nmatrix A the set of x cl~ which are transformed by A to convergent sequences is called the (bounded) summability field of A. A is called regular if its summabflity field contains the convergent sequences and if the limit is preserved. It is well known that the summability field of a regular matrix A is nowhere dense in l~. It is our conjecture that the summability field of a regular A is so thin that the union of countably many such sets is still nowhere dense in l~. In this note we do not prove the full conjecture but show that for a countable set of regular, nonnegative, matrices the union of their summability fields is nondense in l~.
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