This article is cited in 5 papers

Conditionally convergent series in a uniformly smooth Banach space

V. P. Fonf

Khar'kov Branch of the All-Union Design and Scientific-Research Institute of Industrial Transport

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 $\sum x_k$ in the uniformly smooth Banach space $X$ with modulus of smoothness $\rho(t)$, satisfying the condition $\sum\rho(||x_k||)<\infty$.

UDC: 513.88

Received: 12.10.1970

 English version: Mathematical Notes, 1972, 11:2, 129–132

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