Three constructive examples of separable pre-Hilbert spaces nonisomorphic to their closed hyperplanes

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Abstract

An example of a sigma -compact infinite-dimensional pre-Hilbert space H is constructed such that any continuous linear operator T: H --> H is of the form T = lambdaI + F for some lambda is an element of R and for a finite-dimensional continuous linear operator F. A class of simple examples of pre-Hilbert spaces nonisomorphic to their closed hyperplanes is given. A sigma -compact pre-Hilbert space H isomorphic to H x R x R and nonisomorphic to H x R is also constructed.
Original languageEnglish
Pages (from-to)106-121
Number of pages16
JournalRussian Journal of Mathematical Physics
Volume8
Issue number1
Publication statusPublished - Jan 2001

ASJC Scopus subject areas

  • Mathematical Physics
  • Physics and Astronomy(all)
  • Statistical and Nonlinear Physics

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