Abstract.
Aim of this short paper is to construct in any infinite-dimensional Hilbert space a series with terms tending to zero such that some of its rearrangements possess the discrete set of limit points.
The authors would like to express their gratitude to the reviewer for the essential and valuable remarks which helped to improve the paper.
Received: 2012-12-2
Revised: 2013-7-16
Accepted: 2013-8-22
Published Online: 2014-4-17
Published in Print: 2014-6-1
© 2014 by Walter de Gruyter Berlin/Boston
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Articles in the same Issue
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- Porosity and the bounded linear regularity property
- Analytic in planar domains functions with preassigned asymptotic set
- Multiplication of the distributions (x±i0)z
- Hermite–Hadamard type inequalities for extended s-convex functions on the co-ordinates in a rectangle
- Modes of ideal continuity and the additive property in the Riesz space setting
- On complex Fermi curves of two-dimensional, periodic Schrödinger operators
- On the geometrical properties of some classes of complex harmonic functions defined by analytic or coefficient conditions with complex parameter
- On the order of weighted approximation of unbounded functions by some generalizations of Gadjiev–Ibragimov operators
- On series whose rearrangements possess discrete sets of limit points
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Keywords for this article
Series in Banach space;
rearrangements of series;
sets of
limit points
Articles in the same Issue
- Frontmatter
- Porosity and the bounded linear regularity property
- Analytic in planar domains functions with preassigned asymptotic set
- Multiplication of the distributions (x±i0)z
- Hermite–Hadamard type inequalities for extended s-convex functions on the co-ordinates in a rectangle
- Modes of ideal continuity and the additive property in the Riesz space setting
- On complex Fermi curves of two-dimensional, periodic Schrödinger operators
- On the geometrical properties of some classes of complex harmonic functions defined by analytic or coefficient conditions with complex parameter
- On the order of weighted approximation of unbounded functions by some generalizations of Gadjiev–Ibragimov operators
- On series whose rearrangements possess discrete sets of limit points
- A system of two conservation laws with flux conditions and small viscosity