A Lebesgue-type decomposition for non-positive sesquilinear forms
arXiv:1803.02772 · doi:10.1007/s10231-018-0773-5
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.
18 pages