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In mathematics, a nuclear operator is a compact operator for which a trace may be defined, such that the trace is finite and independent of the choice of basis (at least on well behaved spaces; there are some spaces on which nuclear operators do not have a trace). Nuclear operators are essentially the same as trace class operators, though most authors reserve the term "trace class operator" for the special case of nuclear operators on Hilbert spaces. The general definition for Banach spaces was given by Grothendieck. This article presents both cases concentrates on the general case of nuclear operators on Banach spaces; for more details about the important special case of nuclear (=trace class) operators on Hilbert space see the article on trace class operators. ==Compact operator== An operator on a Hilbert space : is compact if it can be written in the form : where and and are (not necessarily complete) orthonormal sets. Here, are a set of real numbers, the singular values of the operator, obeying if . The bracket is the scalar product on the Hilbert space; the sum on the right hand side must converge in norm. An operator that is compact as defined above is said to be nuclear or trace-class if : 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「nuclear operator」の詳細全文を読む スポンサード リンク
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