Numerische Mathematik

, Volume 19, Issue 3, pp 206–208 | Cite as

A note on sub-multiplicative norms

  • P. Lancaster


IfX is a finite-dimensional linear space andL(X) the linear space of linear operators onX thenL(X) may be represented asXX*. IfE={e1, ...,e n } is a basis forX and ∑e j y j * is a typical element ofXX*, then norms can be introduced onL(X) in the form ‖∑‖y j * e j . Given that the norm onX isE-absolute we derive a necessary and sufficient condition for the norm onL(X) to be submultiplicative.


Linear Operator Mathematical Method Linear Space Typical Element 
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  1. 1.
    Lancaster, P., Farahat, H. K.: Norms on direct sums and tensor products. (To appear in Math. Comp.)Google Scholar
  2. 2.
    Maitre, J. F.: Norme composée et norme associéc généralisée d'une matrice. Num. Math.10, 132–141 (1967).Google Scholar

Copyright information

© Springer-Verlag 1972

Authors and Affiliations

  • P. Lancaster
    • 1
  1. 1.Department of Mathematics, Statistics and Computing ScienceThe University of CalgaryCalgaryCanada

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