Research ArticleOpen accessIn the keywordsMeasurable Functional Calculi and Spectral TheoryMykola YaremenkoIn 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 … …Journal of Mathematics and Statistics, Vol. 18, Issue 1 · 6 Jul 2022 · 6,419 accessesView PDFCite
Research ArticleOpen accessIn the abstractLocal Large Deviations: A McMillian Theorem for Typed Random Graph ProcessesKwabena Doku-AmponsahFor a finite typed graph on n nodes and with type law µ on finite alphabet Γ, we define the spectral potential ρλ(., µ), of the graph. From the ρλ(., µ) we define the Kullback action or the divergence function, Hλ(π || v), with respect to an empirical link measure, π, as the Legendre dual. For the finite typed random … …Journal of Mathematics and Statistics, Vol. 13, Issue 4 · 29 Nov 2017 · 7,114 accessesView PDFCite
Research ArticleOpen accessIn the abstractWeyl’s Theorem for Algebraically Class A(s, t) OperatorsD. Senthilkumar, D. KiruthikaIn this study, we show that Weyl’s theorem holds for algebraically class A (s, t) operator acting on Hilbert space. We prove: (i) Weyl’s theorem holds for f (T) for every f belongs to holomorphic function of spectrum of T; (ii) generalized Weyl’s theorem holds for T; (iii) the spectral mapping theorem holds for the Weyl spectrum of T and … …Journal of Mathematics and Statistics, Vol. 8, Issue 1 · 13 Feb 2012 · 6,992 accessesView PDFCite
Research ArticleOpen accessIn the abstractWeyl's Type Theorems for Quasi-Class A OperatorsM.H.M. Rashid, M.S.M. Noorani, A.S. SaariA variant of Weyl theorem for a class of quasi-class A acting on an infinite complex Hilbert space were discussed. If the adjoint of T is a quasi-class A operator, then the generalized a-Weyl holds for f(T) , for every function that analytic on the spectrum of T. The generalized Weyl theorem holds for a quasi-class A was proved. Also, … …Journal of Mathematics and Statistics, Vol. 4, Issue 2 · 30 Jun 2008 · 7,221 accessesView PDFCite