Measurable Functional Calculi and Spectral Theory
- 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.
DOI: https://doi.org/10.3844/jmssp.2022.78.86
Copyright: © 2022 Mykola Yaremenko. This is an open access article distributed under the terms of the
Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.
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Keywords
- Functional Calculus
- Banach Space
- Spectral Theorem
- C*-Algebra
- Measurable Space
- Spectral Integral
- Well-Bounded Operator