## 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 T e 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 V2 , . . . , Yn of spectral maximal

that ...

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 V2 , . . . , Yn of spectral maximal

**subspaces**of T suchthat ...

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### Contents

SPECTRAL OPERATORS | 1924 |

An Operational Calculus for Bounded Spectral | 1941 |

Part | 1950 |

Copyright | |

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adjoint operator analytic apply arbitrary assume B-space Banach space Boolean algebra Borel sets boundary conditions bounded bounded operator Chapter clear closed commuting compact complex consider constant contained continuous converges Corollary corresponding countably additive defined Definition denote dense determined differential operator discrete domain elements equation equivalent established example exists extension fact finite follows formal formula given gives Hence Hilbert space hypothesis identity inequality integral invariant inverse Lemma limit linear linear operator Math Moreover multiplicity norm 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 uniform uniformly unique valued vector weakly zero