Spaceability of subsets of the disc algebra. (English) Zbl 1515.30010
Summary: In this paper we analyse the topological and linear structure of different subsets of the disc algebra. Among others, we consider the set of functions in the disc algebra having a Taylor series about 0 which is unboundedly divergent on a given subset of the unit circle of vanishing arc length measure, and the subsets of functions having uniformly bounded or uniformly convergent Taylor series on the unit circle.
MSC:
| 30B30 | Boundary behavior of power series in one complex variable; over-convergence |
| 30H50 | Algebras of analytic functions of one complex variable |
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