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Standard Models of Abstract Intersection Theory for Operators in Hilbert Space

Grzegorz BanaszakYoichi Uetake — 2015

Bulletin of the Polish Academy of Sciences. Mathematics

For an operator in a possibly infinite-dimensional Hilbert space of a certain class, we set down axioms of an abstract intersection theory, from which the Riemann hypothesis regarding the spectrum of that operator follows. In our previous paper (2011) we constructed a GNS (Gelfand-Naimark-Segal) model of abstract intersection theory. In this paper we propose another model, which we call a standard model of abstract intersection theory. We show that there is a standard model of abstract intersection...

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