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arXiv · 1406.6635

A Short-type Decomposition Of Forms

Zoltán Sebestyén·Zsigmond Tarcsay·Tamás Titkos
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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 $\ast$-algebra.

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Zoltán Sebestyén, Zsigmond Tarcsay, Tamás Titkos. 2014-06-25. A Short-type Decomposition Of Forms. https://arxiv.org/abs/1406.6635

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