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ON THE ORDER STRUCTURE OF REPRESENTABLE FUNCTIONALS

Published online by Cambridge University Press:  04 September 2017

ZSIGMOND TARCSAY
Affiliation:
Department of Applied Analysis, Eötvös L. University, Pázmány Péter sétány 1/c, Budapest H-1117, Hungary e-mail: tarcsay@cs.elte.hu
TAMÁS TITKOS
Affiliation:
Alfréd Rényi Institute of Mathematics, Hungarian Academy of Sciences, Reáltanoda utca 13-15, Budapest H-1053, Hungary e-mail: titkos.tamas@renyi.mta.hu

Abstract

The main purpose of this paper is to investigate some natural problems regarding the order structure of representable functionals on *-algebras. We describe the extreme points of order intervals, and give a non-trivial sufficient condition to decide whether or not the infimum of two representable functionals exists. To this aim, we offer a suitable approach to the Lebesgue decomposition theory, which is in complete analogy with the one developed by Ando in the context of positive operators. This tight analogy allows to invoke Ando's results to characterize uniqueness of the decomposition, and solve the infimum problem over certain operator algebras.

Type
Research Article
Copyright
Copyright © Glasgow Mathematical Journal Trust 2017 

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ON THE ORDER STRUCTURE OF REPRESENTABLE FUNCTIONALS
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