Isomorphisms

  • Paul Richard Halmos
  • Viakalathur Shankar Sunder
Part of the Ergebnisse der Mathematik und ihrer Grenzgebiete book series (MATHE2, volume 96)

Abstract

Is there an integral operator on L 2(II) that is a projection of infinite rank? For ℝ+ the answer is yes (Example 5.1), but the construction seems to make use of the infinite amount of room in ℝ+, i.e., of the infinite measure. The answer is yes for II also, and the proof is not difficult, but it is better understood and more useful if instead of being attacked head on, it is embedded into a larger context.

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Copyright information

© Springer-Verlag Berlin Heidelberg 1978

Authors and Affiliations

  • Paul Richard Halmos
    • 1
  • Viakalathur Shankar Sunder
    • 2
  1. 1.Indiana UniversityBloomingtonUSA
  2. 2.University of CaliforniaSanta BarbaraUSA

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