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

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Page 2094

Restrictions and quotients . Theorem 3 . 10 shows that if a spectral operator Te B

( X ) is reduced by a closed

if T commutes with some projection of X onto Y ) , then the restriction T Y of T to ...

Restrictions and quotients . Theorem 3 . 10 shows that if a spectral operator Te B

( X ) is reduced by a closed

**subspace**y 9 X and one of its complements ( that is ,if T commutes with some projection of X onto Y ) , then the restriction T Y of T to ...

Page 2113

Thus the restriction of an operator T to an arbitrary invariant closed

may have spectrum larger than o ( T ) . Foiaş [ 12 ] defined a closed linear

V is ...

Thus the restriction of an operator T to an arbitrary invariant closed

**subspace**may have spectrum larger than o ( T ) . Foiaş [ 12 ] defined a closed linear

**subspace**Y of a B - space X to be a spectral maximal**subspace**of Te B ( X ) if ( i )V is ...

Page 2114

17 ) and if E , is the corresponding projection operator , then E , X is a spectral

maximal

of o ( T ) there is a family Yı , . . . , Yn of spectral maximal

( i ) ...

17 ) and if E , is the corresponding projection operator , then E , X is a spectral

maximal

**subspace**of T . Hence both ... if for every finite open cover G1 , . . . , Gnof o ( T ) there is a family Yı , . . . , Yn of spectral maximal

**subspaces**of T such that( i ) ...

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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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### Common terms and phrases

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