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Numerische Mathematik

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

A note on sub-multiplicative norms

  • P. Lancaster
Article

Summary

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.

Keywords

Linear Operator Mathematical Method Linear Space Typical Element 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  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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