Vol. 63, No. 2, 1976

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Matrix transformations and absolute summability

Thomas Alan Keagy

Vol. 63 (1976), No. 2, 411–415

The main results of this paper are two theorems which give necessary conditions for a matrix to map into l the set of all subsequences (rearrangements) of a null sequence not in l. These results provide affirmative answers to the following questions proposed by J. A. Fridy. Is a null sequence x necessarily in l if there exists a sum-preserving ll matrix A that maps all subsequences (rearrangements) of x into l?

Mathematical Subject Classification 2000
Primary: 40C05
Received: 23 October 1975
Published: 1 April 1976
Thomas Alan Keagy