Matrix representations for linear transformations on analytic sequences

Philip C. Tonne

Vol. 46 (1973), No. 1, 269–274

DOI: 10.2140/pjm.1973.46.269

Abstract

Let 𝒜 be the space of all analytic sequences, those complex sequences α for which there is a positive number r such that ∑ α_nrⁿ 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

Milestones

Received: 6 January 1972

Published: 1 May 1973