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Refinements of PIP-Spaces

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Part of the Lecture Notes in Mathematics book series (LNM,volume 1986)

Abstract

We have seen in Section 1.5, that the compatibility relation underlying a pip-space may always be coarsened, but not refined in general. There is an exception, however, namely the case of a scale of Hilbert spaces and analogous structures. We shall describe it in this section.

Keywords

  • Hilbert Space
  • Unbounded Operator
  • Spectral Theorem
  • Regular Operator
  • Quadratic Interpolation

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Correspondence to Jean-Pierre Antoine .

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© 2009 Springer-Verlag Berlin Heidelberg

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Antoine, JP., Trapani, C. (2009). Refinements of PIP-Spaces. In: Partial Inner Product Spaces. Lecture Notes in Mathematics(), vol 1986. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-05136-4_5

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