@article {10.3844/jmssp.2022.78.86,
article_type = {journal},
title = {Measurable Functional Calculi and Spectral Theory},
author = {Yaremenko, Mykola},
volume = {18},
year = {2022},
month = {Jul},
pages = {78-86},
doi = {10.3844/jmssp.2022.78.86},
url = {https://thescipub.com/abstract/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.},
journal = {Journal of Mathematics and Statistics},
publisher = {Science Publications}
}