Research Article Open Access

Measurable Functional Calculi and Spectral Theory

Mykola Yaremenko1
  • 1 Department of Partial Differential Equations, the National Technical University of Ukraine, “Igor Sikorsky Kyiv Polytechnic Institute”, Kyiv, Ukraine

Abstract

In this article, the spectral theory is considered, we study the spectral families and their correspondence to the operators on the reflexive Banach spaces; assume A is a well-bounded operator on reflexive Lebesgue spaces then the operator A is a scalar type spectral operator. The main goals are to obtain the characterization of the well-bounded operators in the terms of the associated spectral family in the topology of dual pairing and to construct the continuous functional calculus for well-bounded operators on the Lebesgue space.

Journal of Mathematics and Statistics
Volume 18 No. 1, 2022, 78-86

DOI: https://doi.org/10.3844/jmssp.2022.78.86

Submitted On: 25 November 2021 Published On: 6 July 2022

How to Cite: Yaremenko, M. (2022). Measurable Functional Calculi and Spectral Theory. Journal of Mathematics and Statistics, 18(1), 78-86. https://doi.org/10.3844/jmssp.2022.78.86

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Keywords

  • Functional Calculus
  • Banach Space
  • Spectral Theorem
  • C*-Algebra
  • Measurable Space
  • Spectral Integral
  • Well-Bounded Operator