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Discontinuous subnorms

Goldberg, Moshe and Luxemburg, W. A. J. (2001) Discontinuous subnorms. Linear and Multilinear Algebra, 49 (1). pp. 1-24. ISSN 0308-1087. https://resolver.caltech.edu/CaltechAUTHORS:20181003-135909209

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Abstract

Let S be a subset of a finite-dimensional algebra over a field F either R or C so that S is closed under scalar multiplication. A real-valued function f defined on S, shall be called a subnorm if f(a) > 0 for all 0 ≠ a ε S, and f(αa) = for all a ε S and α ε F. If in addition S is closed under raising to powers, and f(am )=f(a)m for all a ε S and m = 1,2,3,⋯, then f shall be called a submodulus. Further, if S is closed under multiplication, then a submodulus f shall be called a modulus if f(ab) = f(a)f(b) for all a,b ε S. Our main purpose in this paper is to construct discontinuous subnorms, submoduli and moduli, on the complex numbers, the quaternions, and on suitable sets of matrices. In each of these cases we discuss the asymptotic behavior and stability properties of the obtained objects.


Item Type:Article
Related URLs:
URLURL TypeDescription
https://doi.org/10.1080/03081080108818683DOIArticle
Additional Information:© 2001 Taylor & Francis.
Issue or Number:1
Record Number:CaltechAUTHORS:20181003-135909209
Persistent URL:https://resolver.caltech.edu/CaltechAUTHORS:20181003-135909209
Official Citation:Moshe Goldberg & W. A. J. Luxemburg (2001) Discontinuous subnorms, Linear and Multilinear Algebra, 49:1, 1-24, DOI: 10.1080/03081080108818683
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:90102
Collection:CaltechAUTHORS
Deposited By: George Porter
Deposited On:06 Oct 2018 22:17
Last Modified:03 Oct 2019 20:22

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