Vol. 44, No. 1, 1973

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Matrix representations for linear transformations on series analytic in the unit disc

Philip C. Tonne

Vol. 44 (1973), No. 1, 385–392

Let S be the space of all complex sequences A such that if z is a complex number and |z| < 1 then Anzn converges. We present three characterizations of the linear transformations from S to S which have matrix representations. We also characterize the linear transformations from S to the bounded sequences (or to the convergent sequences) which have matrix representations. The characterizations are in terms of natural topologies for the spaces.

Mathematical Subject Classification 2000
Primary: 30A98
Secondary: 46E10
Received: 23 July 1971
Published: 1 January 1973
Philip C. Tonne