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Session 36. Topology in Functional Analysis
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The group \(c_0(X)\) of null sequences of a topological group \(X\) |
Elena Martín-Peinador, Complutense University of Madrid, Spain
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The talk is based on the joint work with D. Dikranjan and V. Tarieladze
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If \(\mathbb{T}\) denotes the circle group, and \(G: = c_0(\mathbb T)\) the group of its null sequences endowed with the uniform topology, then \(G\) is a Pontryagin reflexive metrizable monothetic group with some striking properties which make it paradigmatic.
In this talk we shall concentrate on cardinality aspects of its dual group \(G^\wedge\), and we will study groups of the form \(c_0(X)\) where \(X\) is a compact metrizable topological group.
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References- D. Dikranjan, E. Martín-Peinador, V. Tarieladze, Group valued null sequences and metrizable non-Mackey
groups ,
Forum Math. 26, 2014, 723 - 757.
- D. Dikranjan, E. Martín-Peinador and V. Tarieladze,
Countable powers of topological groups: the uniform topology and cardinality of dual groups , Preprint: ArXiv 1305.7369v1. 31st May 2013
- J. M. Díaz Nieto, E. Martín-Peinador,
Characteristics of the Mackey topology for abelian topological groups ,
Chapter 7 of the book: ``Descriptive Topology and Functional Analysis"
Eds: Juan Carlos Ferrando and Manuel López Pellicer,
``Springer Proceedings in Mathematics and Statistics, 80" (to appear).
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