Arens, Richard and Goldberg, Moshe and Luxemburg, W. A. J. (1992) Multiplicativity factors for seminorms. II. Journal of Mathematical Analysis and Applictions, 170 (2). pp. 401-413. ISSN 0022-247X. doi:10.1016/0022-247X(92)90026-A. https://resolver.caltech.edu/CaltechAUTHORS:20181009-132007385
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Abstract
Let S be a seminorm on an algebra . In this paper we study multiplicativity and quadrativity factors for S, i.e., constants μ > 0 and λ > 0 for which S(xy) ⩽ μS(x)S(y) and S(x2) ⩽ λS(x)2 for all x, y ∈ A. We begin by investigating quadrativity factors in terms of the kernel of S. We then turn to the question, under what conditions does S have multiplicativity factors if it has quadrativity factors? We show that if is commutative then quadrativity factors imply multiplicativity factors. We further show that in the noncommutative case there exist both proper seminorms and norms that have quadrativity factors but no multiplicativity factors.
| Item Type: | Article | ||||||
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| Additional Information: | © 1992 Published by Elsevier Inc. Under an Elsevier user license. Received 25 August 1991. Research supported in part by the Fund for the Promotion of Research at the Technion. | ||||||
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| Issue or Number: | 2 | ||||||
| DOI: | 10.1016/0022-247X(92)90026-A | ||||||
| Record Number: | CaltechAUTHORS:20181009-132007385 | ||||||
| Persistent URL: | https://resolver.caltech.edu/CaltechAUTHORS:20181009-132007385 | ||||||
| Official Citation: | Richard Arens, Moshe Goldberg, W.A.J Luxemburg, Multiplicativity factors for seminorms. II, Journal of Mathematical Analysis and Applications, Volume 170, Issue 2, 1992, Pages 401-413, ISSN 0022-247X, https://doi.org/10.1016/0022-247X(92)90026-A. (http://www.sciencedirect.com/science/article/pii/0022247X9290026A) | ||||||
| Usage Policy: | No commercial reproduction, distribution, display or performance rights in this work are provided. | ||||||
| ID Code: | 90197 | ||||||
| Collection: | CaltechAUTHORS | ||||||
| Deposited By: | Joy Painter | ||||||
| Deposited On: | 10 Oct 2018 18:43 | ||||||
| Last Modified: | 16 Nov 2021 03:30 |
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