Nuclear operators between Banach spaces: Difference between revisions

Revision as of 15:17, 17 September 2015

Revision as of 15:21, 17 September 2015

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is said to be '''nuclear of order ''q'' ''' if there exist sequences of vectors <math>\{g_n\} \in B</math> with <math>\Vert g_n \Vert \le 1</math>, functionals <math>\{f^*_n\} \in A'</math> with <math>\Vert f^*_n \Vert \le 1</math> and [[complex number]]s <math>\{\rho_n\}</math> with

:<math>\inf \left\{ p\ge 1 : \sum_n |\rho_n|^pq < \infty \right\} = q,</math>

such that the operator may be written as