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.
Funding Statement
This work was partially supported by NSF grant DMS 9102965.
Citation
John E. McCarthy. "Geometric interpolation between Hilbert spaces." Ark. Mat. 30 (1-2) 321 - 330, 1992. https://doi.org/10.1007/BF02384878
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