## Linear Operators: Spectral operators |

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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

T commutes with some projection of X onto Y ) , then the restriction T ' | Y of T ...

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

( X ) is reduced by a closed

**subspace**Y şX and one of its complements ( that is , ifT commutes with some projection of X onto Y ) , then the restriction T ' | Y of T ...

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

Y 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 )Y 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 | 1924 |

Spectral Operators | 1925 |

Terminology and Preliminary Notions | 1928 |

Copyright | |

31 other sections not shown

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adjoint operator analytic applications arbitrary assumed B-space Banach space belongs Boolean algebra Borel sets boundary bounded bounded operator Chapter clear closed commuting compact complex condition consider constant contained continuous converges Corollary corresponding countably additive defined Definition denote dense determined 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 perturbation plane positive preceding present problem projections PROOF properties proved range regular resolution resolvent respectively restriction Russian satisfies scalar type seen sequence shown shows similar spectral measure spectral operator spectrum subset subspace sufficiently Suppose Theorem theory topology unbounded uniformly unique valued vector weakly zero