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Title: Compactness of operator integrators
Authors: Titarii Wootijirattikal
Sing Cheong Ong
Yongwimon Lenbury
Ubon Rajathanee University
Mahidol University
Central Michigan University
Center of Excellence in Mathematics
Keywords: Mathematics
Issue Date: 1-Mar-2019
Citation: Operators and Matrices. Vol.13, No.1 (2019), 93-110
Abstract: © 2019, Element D.O.O.. All rights reserved. A function f from a closed interval [a,b] to a Banach space X is a regulated function if one-sided limits of f exist at every point. A function α from [a,b] to the space B(X,Y), of bounded linear transformations form X to a Banach space Y,issaidtobeanintegrator if for each X-valued regulated function f, the Riemann-Stieltjes sums (with sampling points in the interior of subintervals) of f with respect to α converge in Y. We use elementary methods to establish criteria for an integrator α to induce a compact linear transformation from the space, Reg(X), ofX-valued regulated functions to Y. We give direct and elementary proofs for each result to be used, including, among other things, the fact that each integrator α induces a bounded linear transformation, α, from Reg(X) to Y, and other folklore or known results which required reading large amount of literature.
ISSN: 18463886
Appears in Collections:Scopus 2019

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