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+section on nonuniqueness of normal extensions |
→Minimal normal extension: +def of minimal extension |
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B' (\cdots, a_{-2}, a_{-1}, {\hat a_0}, a_1, a_2, \cdots) = (\cdots, - a_{-2}, {\hat a_{-1}}, a_0, a_1, a_2, \cdots).
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Thus one is interested in the normal extension that is, in some sense, smallest. More precisely, a normal operator ''B'' acting on a Hilbert space ''K'' is said to be a '''minimal extension''' of a subnormal ''A'' if '' K' '' ⊂ ''K'' is a reducing subspace of ''B'' and ''H'' ⊂ '' K' '', then ''K' '' = ''K''. (A subspace is a reducing subspace of ''B'' if it is invariant under both ''B'' and ''B*''.)
[[Category:Operator theory]]
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