Conditionally convergent series in a uniformly smooth Banach space

V. P. Fonf

doi:10.1007/BF01097931

Conditionally convergent series in a uniformly smooth Banach space

V. P. Fonf

Research output: Contribution to journal › Article › peer-review

3 Scopus citations

Abstract

The theorem of Steinitz on the form of the set of points which are sums of convergent rearrangements of a given series is extended to series Σx_k in the uniformly smooth Banach space X with modulus of smoothness ρ(t), satisfying the condition Σρ(||x_k||) < ∞.

Original language	English
Pages (from-to)	129-132
Number of pages	4
Journal	Mathematical Notes of the Academy of Sciences of the USSR
Volume	11
Issue number	2
DOIs	https://doi.org/10.1007/BF01097931
State	Published - 1 Jan 1972
Externally published	Yes

ASJC Scopus subject areas

General Mathematics

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title = "Conditionally convergent series in a uniformly smooth Banach space",

abstract = "The theorem of Steinitz on the form of the set of points which are sums of convergent rearrangements of a given series is extended to series Σxk in the uniformly smooth Banach space X with modulus of smoothness ρ(t), satisfying the condition Σρ(||xk||) < ∞.",

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AB - The theorem of Steinitz on the form of the set of points which are sums of convergent rearrangements of a given series is extended to series Σxk in the uniformly smooth Banach space X with modulus of smoothness ρ(t), satisfying the condition Σρ(||xk||) < ∞.

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Conditionally convergent series in a uniformly smooth Banach space

Abstract

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