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===Minimality===
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*''.)<ref name="Conway1991">{{citation|author=John B. Conway|title=The Theory of Subnormal Operators|url=https://books.google.com/books?id=Ho7yBwAAQBAJ&pg=PA38|accessdate=15 June 2017|year=1991|publisher=American Mathematical Soc.|isbn=978-0-8218-1536-6|pages=38–}}</ref>
One can show that if two operators ''B''<sub>1</sub> and ''B''<sub>2</sub> are minimal extensions on ''K''<sub>1</sub> and ''K''<sub>2</sub>, respectively, then there exists a unitary operator
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