2008•Journal of Huzhou Vocational and Technological CollegeRequires access

The Judging Method on Convergence of the Infinite Series in Banach-space

XI Chang-xin

Abstract

We introduce the definition of the convergence in the paper,the absolute convergence in the Banach-space.We discuss the judging method on convergence of the infinite series in the Banach-space in detail.The following conclusions are proved: the infinite series in Banach-space and series of the positive term are equivalent.

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Key concepts: Banach space, Convergence (economics), Series (stratigraphy), Mathematics, Space (punctuation), Unconditional convergence, Infinite-dimensional vector function, Banach manifold