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Zapiski Nauchnykh Seminarov LOMI, 1979, Volume 92, Pages 230–240 (Mi znsl3200)  

Applications of ultraproducts in operator theory. A simple proof of E. Bishop's theorem

V. V. Peller
Abstract: Using technique of ultraproducts of Banach spaces a simple proof of the following E. Bishop's theorem is presented: the closure in the strong operator topology of the set of normal operators on the Hilbert space coincides with the set of subnormal operators. The article contains also some other applications of untraproducts in operator theory (existence of dilation,characterization of spectral measures in Hilbert spaces, similarity of operators, and others).
Bibliographic databases:
UDC: 513.881
Language: Russian
Citation: V. V. Peller, “Applications of ultraproducts in operator theory. A simple proof of E. Bishop's theorem”, Investigations on linear operators and function theory. Part IX, Zap. Nauchn. Sem. LOMI, 92, "Nauka", Leningrad. Otdel., Leningrad, 1979, 230–240
Citation in format AMSBIB
\Bibitem{Pel79}
\by V.~V.~Peller
\paper Applications of ultraproducts in operator theory. A~simple proof of E.~Bishop's theorem
\inbook Investigations on linear operators and function theory. Part~IX
\serial Zap. Nauchn. Sem. LOMI
\yr 1979
\vol 92
\pages 230--240
\publ "Nauka", Leningrad. Otdel.
\publaddr Leningrad
\mathnet{http://mi.mathnet.ru/znsl3200}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=566752}
\zmath{https://zbmath.org/?q=an:0429.47014}
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