A Short-type Decomposition Of Forms
Functional Analysis
2014-06-26 v1
Abstract
The main purpose of this paper is to present a decomposition theorem for nonnegative sesquilinear forms. The key notion is the short of a form to a linear subspace. This is a generalization of the well-known operator short defined by M. G. Krein. A decomposition of a form into a shorted part and a singular part (with respect to an other form) will be called short-type decomposition. As applications, we present some analogous results for bounded positive operators acting on a Hilbert space; for additive set functions on a ring of sets; and for representable positive functionals on a -algebra.
Cite
@article{arxiv.1406.6635,
title = {A Short-type Decomposition Of Forms},
author = {Zoltán Sebestyén and Zsigmond Tarcsay and Tamás Titkos},
journal= {arXiv preprint arXiv:1406.6635},
year = {2014}
}