Measurable Functional Calculi and Spectral Theory
Mykola Yaremenko1 Show affiliations
- Department of Partial Differential Equations, the National Technical University of Ukraine, “Igor Sikorsky Kyiv Polytechnic Institute”, Kyiv, Ukraine
Journal of Mathematics and Statistics, Volume 18, Issue 1, pp. 78–86 · doi.org/10.3844/jmssp.2022.78.86
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.
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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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