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Izv. Akad. Nauk SSSR Ser. Mat., 1971, Volume 35, Issue 5, Pages 1159–1170 (Mi izv2152)  

Operator-irreducible symmetric algebras of operators in the $\mathbf\Pi^1$ Pontryagin space

V. I. Liberzon, V. S. Shul'man


Abstract: In this paper we prove that operator-irreducible weakly closed algebras (containing the identity) on $\mathbf\Pi^1$ are reflexive, and construct a canonical model of an arbitrary symmetric operator-irreducible algebra on $\mathbf\Pi^1$ with a bounded norm, which is not (spatially) irreducible.

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English version:
Mathematics of the USSR-Izvestiya, 1971, 5:5, 1168–1179

Bibliographic databases:

UDC: 513.88
MSC: Primary 46L10; Secondary 46L05
Received: 15.10.1970

Citation: V. I. Liberzon, V. S. Shul'man, “Operator-irreducible symmetric algebras of operators in the $\mathbf\Pi^1$ Pontryagin space”, Izv. Akad. Nauk SSSR Ser. Mat., 35:5 (1971), 1159–1170; Math. USSR-Izv., 5:5 (1971), 1168–1179

Citation in format AMSBIB
\Bibitem{LibShu71}
\by V.~I.~Liberzon, V.~S.~Shul'man
\paper Operator-irreducible symmetric algebras of operators in the $\mathbf\Pi^1$ Pontryagin space
\jour Izv. Akad. Nauk SSSR Ser. Mat.
\yr 1971
\vol 35
\issue 5
\pages 1159--1170
\mathnet{http://mi.mathnet.ru/izv2152}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=288593}
\zmath{https://zbmath.org/?q=an:0233.46083}
\transl
\jour Math. USSR-Izv.
\yr 1971
\vol 5
\issue 5
\pages 1168--1179
\crossref{https://doi.org/10.1070/IM1971v005n05ABEH001215}


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  • Известия Академии наук СССР. Серия математическая Izvestiya: Mathematics
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