## Linear Operators: Spectral Theory : Self Adjoint Operators in Hilbert Space, Volume 2 |

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Page 2094

The situation corresponding to an

. However , Fixman [ 1 ] proved that the restriction of a spectral operator T to an

The situation corresponding to an

**invariant**closed subspace of T is not so simple. However , Fixman [ 1 ] proved that the restriction of a spectral operator T to an

**invariant**closed subspace y of X is spectral if and only if the resolution of the ...Page 2214

5 , the weakly closed operator algebra W ( B ) generated by B is the same as the

strongly closed algebra generated by B . Thus every A in W ( B ) is the strong limit

of finite linear combinations of elements of B . It follows that A leaves

5 , the weakly closed operator algebra W ( B ) generated by B is the same as the

strongly closed algebra generated by B . Thus every A in W ( B ) is the strong limit

of finite linear combinations of elements of B . It follows that A leaves

**invariant**...Page 2286

Our final objective is to show that the operator A induces a one - to - one

correspondence between the subspaces of X

closed ...

Our final objective is to show that the operator A induces a one - to - one

correspondence between the subspaces of X

**invariant**under B and those of H**invariant**under B , the resolution of the identity of Q . 37 DEFINITION . If M is aclosed ...

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### Contents

SPECTRAL OPERATORS XV Spectral Operators | 1924 |

Introduction | 1925 |

Terminology and Preliminary Notions | 1928 |

Copyright | |

32 other sections not shown

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analytic apply arbitrary assumed B-space Banach space Boolean algebra Borel sets boundary conditions bounded bounded Borel bounded operator Chapter clear clearly closure commuting compact complex consider constant contained converges Corollary corresponding countably additive defined Definition denote dense determined differential operator domain elements equation equivalent established example exists extension fact finite follows formula given gives Hence Hilbert space hypothesis identity inequality integral invariant inverse Lemma limit linear linear operator manifold Math Moreover multiplicity norm normal positive preceding present problem projections PROOF properties prove range regular resolution resolvent respectively restriction Russian satisfies scalar type seen sequence shown shows spectral measure spectral operator spectrum statement strongly subset subspace sufficiently Suppose Theorem theory topology unbounded uniformly unique valued vector weakly zero