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Matrix representations
for linear transformations on series analytic in the unit
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Philip C. Tonne |
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Vol. 44 (1973), No. 1, 385–392
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Abstract |
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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
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Milestones
Received: 23 July 1971
Published: 1 January 1973
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Authors |
| Philip C. Tonne | |
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