Vol. 46, No. 1, 1973

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Matrix representations for linear transformations on analytic sequences

Philip C. Tonne

Vol. 46 (1973), No. 1, 269–274

Let 𝒜 be the space of all analytic sequences, those complex sequences α for which there is a positive number r such that αnrn converges. Those linear transformations from 𝒜 to 𝒜 which have matrix representations are characterized in terms of various spaces and topologies associated with 𝒜 An example is given of a linear transformation from 𝒜 to 𝒜 which has no matrix representation.

Mathematical Subject Classification 2000
Primary: 46A40
Secondary: 40H05
Received: 6 January 1972
Published: 1 May 1973
Philip C. Tonne