|
In the mathematical field of functional analysis there are several standard topologies which are given to the algebra ''B''(''H'') of bounded linear operators on a Hilbert space ''H''. ==Introduction== Let be a sequence of linear operators on the Hilbert space ''H''. Consider the statement that ''T''''n'' converges to some operator ''T'' in ''H''. This could have several different meanings: * If , that is, the operator norm of ''T''''n'' - ''T'' (the supremum of , where ''x'' ranges over the unit ball in ''H'') converges to 0, we say that in the uniform operator topology. * If for all ''x'' in ''H'', then we say in the strong operator topology. * Finally, suppose in the weak topology of ''H''. This means that for all linear functionals ''F'' on ''H''. In this case we say that in the weak operator topology. All of these notions make sense and are useful for a Banach space in place of the 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「Operator topologies」の詳細全文を読む スポンサード リンク
|