On divergence in category of sequences of linear operators

Rok, strany: 1993, 43 - 50

The subject of this paper is a problem of unbounded divergence in category of sequences of linear operators $\{L_n(f, t)\}$ mapping a $B$-space into a space of continuous functions. The boundedness in category of the sequence $\{L_n(f, t)\}$ proved to be equivalent to boundedness in category of the sequence of linear functionals norms $|L(f)(t)|$.

As a result there exists a function $f$ from a space of functions whose module of continuity does not exceed a majorant of modules of continuity whose Fourier series diverges in category.

ISO 690:

Konovalenko, D. 1993. On divergence in category of sequences of linear operators. In Tatra Mountains Mathematical Publications, vol. 2, no.1, pp. 43-50. 1210-3195.

APA:

Konovalenko, D. (1993). On divergence in category of sequences of linear operators. Tatra Mountains Mathematical Publications, 2(1), 43-50. 1210-3195.