Characterizing the metric compactification of Lp spaces by random measures

Armando W. Gutiérrez

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Abstract

We present a complete characterization of the metric compactification of Lp spaces for 1≤p<∞. Each element of the metric compactification of Lp is represented by a random measure on a certain Polish space. By way of illustration, we revisit the Lp-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 languageEnglish
Article numberAFA-D-19-00059
Number of pages17
JournalAnnals of Functional Analysis
DOIs
Publication statusPublished - 1 Jan 2020
MoE publication typeA1 Journal article-refereed

Keywords

  • Mathematics - Functional Analysis
  • Mathematics - Metric Geometry
  • Mathematics - Probability
  • 54D35
  • 46E30
  • 60G57

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