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Defence of dissertation in the field of Mathematics, Armando Gutierrez, M.Sc.

Metric geometry of Banach spaces observed from infinity

The dissertation "Metric compactification of Banach spaces" contains a detailed overview of the construction of the metric compactification of arbitrary metric spaces followed by complete explicit descriptions of the metric compactification of classical Banach spaces in finite and infinite dimensions. Consequently, some ergodic and fixed point theorems are revisited.

Natural and social phenomena are often modeled by deterministic or random processes. These models can be mathematically described by a collection of mappings acting on certain spaces with a rich structure. Metric spaces are perfect environments where many mathematical models can be analyzed analytically and geometrically. In order to obtain precise knowledge of the model we also need certain topological properties. Compactness is a topological property that is needed in many areas of mathematics. 

The metric compactification is the result of making a metric space into a dense subset of a compact space by adding a boundary at infinity. The elements of the metric compactification have functorial properties and, more importantly, define a weak topology on arbitrary metric spaces that gives a geometric interpretation of points escaping to infinity.

Explicit formulas for all the elements of the metric compactification of classical Banach spaces were presented in this dissertation. In addition, geometric proofs of certain ergodic and fixed point theorems were provided.

Opponent: Dr. Bas Lemmens, University of Kent, UK.

Custos: Professor  Kalle Kytölä, Aalto University School of Science, Department of Mathematics and Systems Analysis.

Contact information: Armando W. Gutiérrez, Department of Mathematics and Systems Analysis, [email protected], +593443075558

Electronic dissertation: http://urn.fi/URN:ISBN:978-952-60-8811-2

The dissertation is publicly displayed 10 days before the defence at the noticeboard of the School of Science in Konemiehentie 2, Espoo.

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