Dense Subspaces in Scales of Hilbert Spaces

  • Volodymyr Koshmanenko
  • Mykola Dudkin
Part of the Operator Theory: Advances and Applications book series (OT, volume 253)


In this chapter we investigate the following question. Under what conditions a subset of a Hilbert space is continuously embedded into another Hilbert space? More precisely, let a couple of Hilbert spaces \(\mathcal{H}, \mathcal{H}_{+}\) be such that \(\mathcal{H}_{+}\) is a proper subset of \(\mathcal{H}_{0}\), i.e., H ⊃ \( \mathcal{H} \sqsupset \mathcal{H}_{+}\).


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Copyright information

© Springer International Publishing Switzerland 2016

Authors and Affiliations

  • Volodymyr Koshmanenko
    • 1
  • Mykola Dudkin
    • 2
  1. 1.Institute of MathematicsNational Academy of Sciences of UkraineKyivUkraine
  2. 2.Kyiv Polytechnic InstituteNational Technical University of UkraineKyivUkraine

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