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In functional analysis, the weak operator topology, often abbreviated WOT, is the weakest topology on the set of bounded operators on a Hilbert space ''H'', such that the functional sending an operator ''T'' to the complex number <''Tx'', ''y''> is continuous for any vectors ''x'' and ''y'' in the Hilbert space. Explicitly, for an operator ''T'' there is base of neighborhoods of the following type: choose a finite number of vectors ''xi'', continuous functionals ''yi'', and constants ''εi'' indexed by the same finite set. An operator ''S'' lies in the neighborhood if and only if ''yi(T(xi) - S(xi)) < εi'' for all ''i''. Equivalently, a net ''Ti'' ⊂ ''B''(''H'') of bounded operators converges to ''T'' ∈ ''B''(''H'') in WOT if for all ''y *'' in ''H *'' and ''x'' in ''H'', the net ''y *''(''Tix'') converges to ''y *''(''Tx''). == Relationship with other topologies on ''B''(''H'') == The WOT is the weakest among all common topologies on ''B''(''H''), the bounded operators on a Hilbert space ''H''. 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「weak operator topology」の詳細全文を読む スポンサード リンク
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