English Scientific Article (Journal Article)

Published: PROCEEDINGS OF THE EDINBURGH MATHEMATICAL SOCIETY 0013-0915 1464-3839 62 (1) pp. 125-133 2019

- SJR Scopus - Mathematics (miscellaneous): Q2

Identifiers

- MTMT: 3256669
- DOI: 10.1017/S0013091518000287
- REAL: 60444
- WoS: 000456171700008
- Scopus: 85053003799
- Mathematical Reviews: MR3938822
- arXiv: 1609.03021

Several Lebesgue-type decomposition theorems in analysis have a strong relation to
the operation called: parallel sum. The aim of this paper is to investigate this relation
from a new point of view. Namely, using a natural generalization of Arlinskii's approach
(which identifies the singular part as a fixed point of a single-variable map) we
prove the existence of a Lebesgue-type decomposition for nonnegative sesquilinear
forms. As applications, we also show that how this approach can be used to derive
analogous results for representable functionals, nonnegative finitely additive measures,
and positive definite operator functions. The focus is on the fact that each theorem
can be proved with the same completely elementary method.

2020-09-20 17:27