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Zap. Nauchn. Sem. POMI, 2000, Volume 270, Pages 90–102 (Mi znsl1329)  

Similarity problem for certain martingale uniform algebras

S. V. Kislyakov

St. Petersburg Department of V. A. Steklov Institute of Mathematics, Russian Academy of Sciences

Abstract: Let $A$ be a proper uniform algebra admitting a nontrivial bounded point derivation. Then for a certain uniform algebra $A_1$ (related to $A$ much as the algebra of Hardy martingales on $\mathbb T^\infty$ is related to the disk algebra) there exists a bounded but not completely bounded homomorphism $\varphi\colon A_1\to B(H)$.

Full text: PDF file (201 kB)

English version:
Journal of Mathematical Sciences (New York), 2003, 115:2, 2141–2146

Bibliographic databases:

UDC: 517.5
Received: 28.03.2000

Citation: S. V. Kislyakov, “Similarity problem for certain martingale uniform algebras”, Investigations on linear operators and function theory. Part 28, Zap. Nauchn. Sem. POMI, 270, POMI, St. Petersburg, 2000, 90–102; J. Math. Sci. (N. Y.), 115:2 (2003), 2141–2146

Citation in format AMSBIB
\Bibitem{Kis00}
\by S.~V.~Kislyakov
\paper Similarity problem for certain martingale uniform algebras
\inbook Investigations on linear operators and function theory. Part~28
\serial Zap. Nauchn. Sem. POMI
\yr 2000
\vol 270
\pages 90--102
\publ POMI
\publaddr St.~Petersburg
\mathnet{http://mi.mathnet.ru/znsl1329}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=1795641}
\zmath{https://zbmath.org/?q=an:1042.46027}
\transl
\jour J. Math. Sci. (N. Y.)
\yr 2003
\vol 115
\issue 2
\pages 2141--2146
\crossref{https://doi.org/10.1023/A:1022880619755}


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