Characterizing the metric compactification of Lp spaces by random measures

Armando W. Gutiérrez

doi:10.1007/s43034-019-00024-1

Characterizing the metric compactification of L_p spaces by random measures

Armando W. Gutiérrez^*

^*Corresponding author for this work

Not published at VTT

Aalto University

Research output: Contribution to journal › Article › Scientific › peer-review

8 Citations (Scopus)

Abstract

We present a complete characterization of the metric compactification of L_p spaces for 1 ≤ p< ∞. Each element of the metric compactification of L_p is represented by a random measure on a certain Polish space. By way of illustration, we revisit the L_p-mean ergodic theorem for 1 < p< ∞, and Alspach’s example of an isometry on a weakly compact convex subset of L₁ with no fixed points.

Original language	English
Pages (from-to)	227-243
Journal	Annals of Functional Analysis
Volume	11
Issue number	2
DOIs	https://doi.org/10.1007/s43034-019-00024-1
Publication status	Published - 1 Apr 2020
MoE publication type	A1 Journal article-refereed

Funding

Open access funding provided by Aalto University. The author is very grateful to Prof. Anders Karlsson, Prof. Kalle Kytölä, and Prof. Olavi Nevanlinna for many valuable discussions and suggestions. The author is also thankful to the anonymous referees for valuable suggestions that improved the presentation of this paper. This work was supported by the Academy of Finland, Grant No. 288318.

Keywords

Banach spaces
horofunction
metric compactification
metric functional
random measure

Access to Document

10.1007/s43034-019-00024-1Licence: CC BY

Cite this

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