Geometric interpolation between Hilbert spaces

John E. McCarthy Department of Mathematics, Washington University

TBD mathscidoc:1701.332777

Arkiv for Matematik, 30, (1), 321-330, 1991.9
We prove that there is a unique way to construct a geometric scale of Hilbert spaces interpolating between two given spaces. We investigate what properties of operators, other than boundedness, are preserved by interpolation. We show that self-adjointness is, but subnormality and Krein subnormality are not. On the way to this last result, we establish a representation theorem for cyclic Krein subnormal operators.
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@inproceedings{john1991geometric,
  title={Geometric interpolation between Hilbert spaces},
  author={John E. McCarthy},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20170108203538665381586},
  booktitle={Arkiv for Matematik},
  volume={30},
  number={1},
  pages={321-330},
  year={1991},
}
John E. McCarthy. Geometric interpolation between Hilbert spaces. 1991. Vol. 30. In Arkiv for Matematik. pp.321-330. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20170108203538665381586.
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