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On regularizers of unbounded linear operators in Banach spaces

Regularizers of densely defined unbounded linear operators in Banach spaces and their applications to spectral theory are considered. Necessary and sufficient conditions in terms of regularizer properties for an unbounded operator T to have discrete spectrum are obtained. In the case where T has a self-adjoint regularizer in some Schatten--von Neumann ideals, asymptotic properties of the eigenvalues are investigated; in particular, it is shown that the eigenvalues of T asymptotically belong to some angle in the complex plane. Bibliography: 16 titles.

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Correspondence to V. M. Kaplitskii.

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Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 401, 2012, pp. 93–102.

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Kaplitskii, V.M. On regularizers of unbounded linear operators in Banach spaces. J Math Sci 194, 651–655 (2013). https://doi.org/10.1007/s10958-013-1554-8

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  • DOI: https://doi.org/10.1007/s10958-013-1554-8

Keywords

  • Banach Space
  • Linear Operator
  • Complex Plane
  • Spectral Theory
  • Asymptotic Property