caa a22 4500 606166262 CHVBK 20210128100657.0 cr unu---uuuuu 210128e20151201xx s 000 0 eng 10.1007/s10440-014-9976-y doi (NATIONALLICENCE)springer-10.1007/s10440-014-9976-y Davison Trubee Department of Mathematics, University of Colorado, Boulder, USA aut Generalizing the Kantorovich Metric to Projection Valued Measures [Elektronische Daten] [Trubee Davison] Given a compact metric space X, the collection of Borel probability measures on X can be made into a compact metric space via the Kantorovich metric (Hutchinson in Indiana Univ. Math. J. 30(5):713-747, 1981). We partially generalize this well known result to projection valued measures. In particular, given a Hilbert space $\mathcal{H}$ , we consider the collection of projection valued measures from X into the projections on $\mathcal{H}$ . We show that this collection can be made into a complete and bounded metric space via a generalized Kantorovich metric. However, we add that this metric space is not compact, thereby identifying an important distinction from the classical setting. We have seen recently that this generalized metric has been previously defined by F. Werner in the setting of mathematical physics (Werner in J. Quantum Inf. Comput. 4(6):546-562, 2004). To our knowledge, we develop new properties and applications of this metric. Indeed, we use the Contraction Mapping Theorem on this complete metric space of projection valued measures to provide an alternative method for proving a fixed point result due to P. Jorgensen (see Adv. Appl. Math. 34(3):561-590, 2005; Operator Theory, Operator Algebras, and Applications, pp.13-26, Am. Math. Soc., Providence, 2006). This fixed point, which is a projection valued measure, arises from an iterated function system on X, and is related to Cuntz Algebras. Springer Science+Business Media Dordrecht, 2014 Kantorovich metric nationallicence Projection valued measure nationallicence Cuntz algebra nationallicence Fixed point nationallicence Acta Applicandae Mathematicae Springer Netherlands 140/1(2015-12-01), 11-22 0167-8019 140:1<11 2015 140 10440 https://doi.org/10.1007/s10440-014-9976-y text/html Onlinezugriff via DOI BK010053 XK010053 XK010000 Metadata rights reserved Springer special CC-BY-NC licence nationallicence 1 research-article jats NATIONALLICENCE NATIONALLICENCE NL-springer NATIONALLICENCE 856 40 https://doi.org/10.1007/s10440-014-9976-y text/html Onlinezugriff via DOI NATIONALLICENCE 100 1- Davison Trubee Department of Mathematics, University of Colorado, Boulder, USA aut NATIONALLICENCE 773 0- Acta Applicandae Mathematicae Springer Netherlands 140/1(2015-12-01), 11-22 0167-8019 140:1<11 2015 140 10440