Norm Estimates for Multiplication Operators in Hilbert Algebras
Matematičeskie zametki, Tome 72 (2002) no. 2, pp. 283-291
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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).
@article{MZM_2002_72_2_a11,
author = {A. N. Urinovskii},
title = {Norm {Estimates} for {Multiplication} {Operators} in {Hilbert} {Algebras}},
journal = {Matemati\v{c}eskie zametki},
pages = {283--291},
year = {2002},
volume = {72},
number = {2},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/MZM_2002_72_2_a11/}
}
A. N. Urinovskii. Norm Estimates for Multiplication Operators in Hilbert Algebras. Matematičeskie zametki, Tome 72 (2002) no. 2, pp. 283-291. http://geodesic.mathdoc.fr/item/MZM_2002_72_2_a11/