On \(\Lambda\)-strong convergence of numerical sequences and Fourier series (Q920328)

The author obtains several results concerning the \(\Lambda\)-strong convergence of numerical sequences and Fourier series. In section 2 the author shows that the class c(\(\Lambda\)) of \(\Lambda\)-strongly convergent sequences of complex numbers endowed with the norm \(\| \cdot \|_{c(\Lambda)}\) is a Banach space and that it has a Schauder basis. Let C be the Banach space of the \(2\pi\) periodic complex-valued continuous functions endowed with the norm \(\| f\|_ C=\max_{t}f(t)\). In section 3 of this paper the author establishes that the class S(\(\Lambda\)) of functions \(f\in C\) whose Fourier series converges uniformly \(\Lambda\)-strongly on [0,2\(\pi\)), endowed with a suitable norm is a Banach space. In section 4, results of section 3 are reformulated by substituting the \(L_ p\)-metric for C-metric.