2014/06/25 by Sebestyén, Zoltán, Tarcsay, Zsigmond, Titkos, Tamás
#28A12 #46L51 #FOS: Mathematics #Functional Analysis (math.FA) #Primary 47A07 #Secondary 47B65
paper · doi:10.48550/arxiv.1406.6635
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.