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Izv. Akad. Nauk SSSR Ser. Mat., 1989, Volume 53, Issue 2, Pages 227–242 (Mi izv1238)  

Diameters of state spaces of Jordan Banach algebras

Sh. A. Ayupov, Sh. M. Usmanov


Abstract: The notion of diameter $D(A)$ of the state space of a Jordan Banach algebra ($JBW$-algebra $A$) is introduced. The diameters of the state spaces for $JBW$-factors of type $\mathrm I_n$ ($n<+\infty$), $\mathrm I_\infty$, $\mathrm{II}_1$, $\mathrm{II}_\infty$, $\mathrm{III}_\lambda$ ($0<\lambda<1$) are computed.
It is proved that if $A$ is not a factor, or is a factor of type $\mathrm I_\infty$ or $\mathrm{II}_1$, then $D(A)=2$. If $A$ is a $JBW$-factor of type $\mathrm I_n$ ($n<+\infty$), then $D(A)=2(1-1/n)$, and if $A$ is a $JBW$-factor of type $\mathrm{III}_\lambda$ ($0<\lambda<1$), then $D(A)=2(1-\sqrt\lambda)/(1+\sqrt\lambda)$ or $D(A)=2(1-\sqrt[4]\lambda)/(1+\sqrt[4]\lambda)$.
Bibliography: 15 titles.

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English version:
Mathematics of the USSR-Izvestiya, 1990, 34:2, 229–244

Bibliographic databases:

UDC: 517.986
MSC: Primary 46L30; Secondary 46L35
Received: 16.06.1987

Citation: Sh. A. Ayupov, Sh. M. Usmanov, “Diameters of state spaces of Jordan Banach algebras”, Izv. Akad. Nauk SSSR Ser. Mat., 53:2 (1989), 227–242; Math. USSR-Izv., 34:2 (1990), 229–244

Citation in format AMSBIB
\Bibitem{AyuUsm89}
\by Sh.~A.~Ayupov, Sh.~M.~Usmanov
\paper Diameters of state spaces of Jordan Banach algebras
\jour Izv. Akad. Nauk SSSR Ser. Mat.
\yr 1989
\vol 53
\issue 2
\pages 227--242
\mathnet{http://mi.mathnet.ru/izv1238}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=998294}
\zmath{https://zbmath.org/?q=an:0716.46049}
\transl
\jour Math. USSR-Izv.
\yr 1990
\vol 34
\issue 2
\pages 229--244
\crossref{https://doi.org/10.1070/IM1990v034n02ABEH000622}


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  • Известия Академии наук СССР. Серия математическая Izvestiya: Mathematics
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