Sublinear function: Difference between revisions

Revision as of 01:43, 13 January 2022

Revision as of 01:46, 13 January 2022

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If <math>p</math> is a real-valued sublinear function on a real vector space <math>X</math> then the map <math>q(x) := \max \{p(x), p(- x)\}</math> defines a [[seminorm]] on <math>X</math> called the '''seminorm associated with <math>p.</math>'''{{sfn|Narici|Beckenstein|2011|pp=120-121}}

TheA sublinear function <math>p</math> on a real or complex vector space is a [[#symmetric function|symmetric function]] if and only if <math>p = q</math> (where <math>q(x) := \max \{p.(x), p(- x)\}</math> as before).

===Relation to linear functionals===