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7 Functions of Non-compact Operators

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Part of the Lecture Notes in Mathematics book series (LNM,volume 1830)

Abstract

The present chapter is concerned with the estimates for the norms of resolvents and analytic functions of so called P-triangular operators. Roughly speaking, a P-triangular operator is a sum of a normal operator and a compact quasinilpotent one, having a sufficiently rich set of invariant subspaces. In particular, we consider the following classes of P-triangular operators: operators whose Hermitian components are compact operators, and operators, which are represented as sums of unitary operators and compact ones.

Keywords

  • Regular Point
  • Unbounded Operator
  • Diagonal Part
  • Volterra Operator
  • Closed Convex Hull

These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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© 2003 Springer-Verlag Berlin Heidelberg

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Gil’, M.I. (2003). 7 Functions of Non-compact Operators. In: Operator Functions and Localization of Spectra. Lecture Notes in Mathematics, vol 1830. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-45225-6_7

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  • DOI: https://doi.org/10.1007/978-3-540-45225-6_7

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-20246-2

  • Online ISBN: 978-3-540-45225-6

  • eBook Packages: Springer Book Archive