Riemann–Stieltjes Integration of Operator-Valued Functions with Respect to Vector-Valued Functions in Banach Spaces

descriptionPublicationkeyboard_double_arrow_right Article 01 May 1972 English Publisher:Society for Industrial & Applied Mathematics (SIAM)Journal:SIAM Journal on Mathematical Analysis, volume 3, pages 183-205 (issn: 0036-1410, eissn: 1095-7154,

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Authors: Prugovecki, Eduard;

doi: 10.1137/0503020

Riemann–Stieltjes Integration of Operator-Valued Functions with Respect to Vector-Valued Functions in Banach Spaces

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Abstract

The concept of Riemann–Stieltjes integrals is generalized to operator-valued integrands and with respect to vector-valued functions. Integrals of this type appear in perturbation theory of linear operators and in quantum scattering theory. Different versions of such integrals are defined and their existence for given classes of functions is investigated. Some simple examples are explicitly considered.

Keywords

Vector-valued set functions, measures and integrals, Vector-valued measures and integration, Integrals of Riemann, Stieltjes and Lebesgue type

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