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Geometric interpolation between Hilbert spaces

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Arkiv för Matematik

Abstract

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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Authors and Affiliations

  1. Department of Mathematics, Washington University, 63130, St. Louis, MO, U.S.A.

    John E. McCarthy

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  1. John E. McCarthy
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Additional information

This work was partially supported by NSF grant DMS 9102965.

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McCarthy, J.E. Geometric interpolation between Hilbert spaces. Ark. Mat. 30, 321–330 (1992). https://doi.org/10.1007/BF02384878

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  • DOI: https://doi.org/10.1007/BF02384878

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