Sequences of the Projection-valued Measures and Functional Calculi


  • Mykola Ivanovich Yaremenko Department of Partial Differential Equations, Faculty of Mathematics and Physics, The National Technical University of Ukraine, 04213, Kyiv, Ukraine



functional calculus, projection-valued measure, projection operator, measurable calculus


Let a pair  be functional calculus, where  is a homomorphism from the space of the measurable functions on  into the space of all linear bounded operators  on a reflexive Banach space . We define a norm of functional calculus  by , the convergence of the sequence of functional calculi is a convergence relative to this norm. We study the correspondence between sequences of spectral decompositions, well-bounded operators  defined on the reflexive Banach space , and their correspondence with the theory of functional calculus for such operators. In this article, we establish that if a sequence of the projection-valued measures  strongly converges to  then the sequence  of the functional calculi converges to the functional calculus  Results of the article can be employed in the modern extensions of the quantum theory and theory of quantum information.    


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How to Cite

Yaremenko, M. I. (2023). Sequences of the Projection-valued Measures and Functional Calculi. Journal of Science and Mathematics Letters, 11(2), 39–47.