Thenumber of points where a linear mapping from   into   attains its norm

doi:10.1285/i15900932v12p145

Thenumber of points where a linear mapping from $ln2$ into $lnp$ attains its norm

Werner Linde

Abstract

Let S be a regular $n n$ -matrix mapping $l2n$ onto $lpn$ , $1≤ p < ∈fty$ , with norm(Error rendering LaTeX formula). Then we are interested in the set (Error rendering LaTeX formula) i.e. the set of points on the unit sphere where S attains its norm. We prove $card(C) <∈fty$ for $1≤ p < 2$ .This follows from properties of the Taylor expansion of $x → \|Sx\|p$ near points in C. The case $2 2$ the behaviour of $x → \|Sx\|p$ may be completely different as for $p < 2$ .

DOI Code: 10.1285/i15900932v12p145

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Note di Matematica

Thenumber of points where a linear mapping from $l<sup>n</sup><sub>2</sub>$ into $l<sup>n</sup><sub>p</sub>$ attains its norm

Abstract

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