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A Lebesgue-type decomposition for non-positive sesquilinear forms (1803.02772v1)

Published 7 Mar 2018 in math.FA

Abstract: A Lebesgue-type decomposition of a (non necessarily non-negative) sesquilinear form with respect to a non-negative one is studied. This decomposition consists of a sum of three parts: two are dominated by an absolutely continuous form and a singular non-negative one, respectively, and the latter is majorized by the product of an absolutely continuous and a singular non-negative forms. The Lebesgue decomposition of a complex measure is given as application.

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