Series in Banach and Hilbert Spaces

Elzbieta Kraszewska

Warsaw University, Bialystok

Jan Popiolek

Warsaw University, Bialystok

Summary.

In [14] the series of real numbers were investigated. The introduction to Banach and Hilbert spaces ([10], [11],[12]), enables us to arrive at the concept of series in Hilbert space. We start with the notions: partial sums of series, sum and $n$-th sum of series, convergent series (summable series), absolutely convergent series. We prove some basic theorems: the necessary condition for a series to converge, Weierstrass' test, d'Alembert's test, Cauchy's test.

MML Identifier: BHSP_4

Contents (PDF format)

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