Weak trace-class operator: Difference between revisions

Revision as of 03:06, 13 July 2014

Revision as of 03:08, 24 March 2015

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== Definition ==

A [[compact operator]] ''A'' on an infinite dimensional [[separable space|separable]] [[Hilbert space]] ''H'' is ''weak trace class'' if μ(''n'',''A'') {{=}} O(''n''⁻¹), where μ(''A'') is the sequence of [[singular value]]s. In mathematical notation the two-sided [[ideal (ring theory)|ideal]]{{dn|date=July 2014}} of all weak trace-class operators is denoted,

::::<math> L_{1,\infty} = \{ A \in K(H) : \mu(n,A) = O(n^{-1}) \}. </math>