On divergence in category of sequences of linear operators. (English) Zbl 0799.28002
The notion of the convergence in category has been introduced by E. Wagner [Rend. Accad. Sci. Fis. Mat., IV. Ser., Napoli 45, 303-312 (1978; Zbl 0463.28002)]. This paper deals with the convergence in category of a sequence of linear operators giving a necessary and sufficient condition for this convergence. As a corollary there is given an example of a function from \(H^ \omega\) having a Fourier series which diverges in category.
Reviewer: W.Wilczyński (Łódź)
MSC:
| 28A20 | Measurable and nonmeasurable functions, sequences of measurable functions, modes of convergence |
| 42A20 | Convergence and absolute convergence of Fourier and trigonometric series |
