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 Mat. Zametki, 2002, Volume 72, Issue 2, Pages 283–291 (Mi mz422)

Norm Estimates for Multiplication Operators in Hilbert Algebras

A. N. Urinovskii

M. V. Lomonosov Moscow State University

Abstract: In this paper, it is proved that for the bilinear operator defined by the operation of multiplication in an arbitrary associative algebra $\mathbf V$ with unit $\mathbf e_0$ over the fields $\mathbb R$ or $\mathbb C$, the infimum of its norms with respect to all scalar products in this algebra (with $||\mathbf e_0||=1$) is either infinite or at most $\sqrt {4/3}$. Sufficient conditions for this bound to be not less than $\sqrt {4/3}$ are obtained. The finiteness of this bound for infinite-dimensional Grassmann algebras was first proved by Kupsh and Smolyanov (this was used for constructing a functional representation for Fock superalgebras).

DOI: https://doi.org/10.4213/mzm422

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English version:
Mathematical Notes, 2002, 72:2, 253–260

Bibliographic databases:

UDC: 517.986.22

Citation: A. N. Urinovskii, “Norm Estimates for Multiplication Operators in Hilbert Algebras”, Mat. Zametki, 72:2 (2002), 283–291; Math. Notes, 72:2 (2002), 253–260

Citation in format AMSBIB
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• http://mi.mathnet.ru/eng/mz/v72/i2/p283

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This publication is cited in the following articles:
1. Xia Xintao, Chen Xiaoyang, Wang Zhongyu, Zhang Yongzhen, “Norm Theory of Error Separation and its Application to Harmonic Distribution Parameters of Rolling Bearing Surfaces - Art. No. 63572M”, Signal Analysis, Measurement Theory, Photo-Electronic Technology, and Artificial Intelligence, Pts 1 and 2, Proceedings of the Society of Photo-Optical Instrumentation Engineers (SPIE), 6357, no. Part 1-2, eds. Fang J., Wang Z., SPIE-Int Soc Optical Engineering, 2006, 63572M, M3572
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