A note on sub-multiplicative norms |
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Authors: | P Lancaster |
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Institution: | (1) Department of Mathematics, Statistics and Computing Science, The University of Calgary, Calgary, Alberta, Canada |
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Abstract: | Summary IfX is a finite-dimensional linear space andL(X) the linear space of linear operators onX thenL(X) may be represented asXX
*. IfE={e
1, ...,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. |
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Keywords: | |
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