## Linear Operators: Part III: Spectral Operators [by] Nelson Dunford and Jacob T. Schwartz, with the Assistance of William G. Bade and Robert G. Bartle, Volume 1 |

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Page 1960

sum HP of a Hilbert space H with itself p times whose matrix representation ( Quy

) has , for its

algebra A of operators on H . Only a few basic properties of the algebra AP and ...

sum HP of a Hilbert space H with itself p times whose matrix representation ( Quy

) has , for its

**elements**, the operators diy which all belong to a commutative B * -algebra A of operators on H . Only a few basic properties of the algebra AP and ...

Page 1966

... that B ( EP ) is a B * - algebra ( IX . 3 . 2 ) . Just as was the case with eBIS , 2 )

the

and Ể are equivalent if Â ( s ) = ( s ) Ể for e - almost all s in S . For a given matrix Â

...

... that B ( EP ) is a B * - algebra ( IX . 3 . 2 ) . Just as was the case with eBIS , 2 )

the

**elements**of the algebra û ” are equivalence classes where two matrices Âand Ể are equivalent if Â ( s ) = ( s ) Ể for e - almost all s in S . For a given matrix Â

...

Page 2512

On the completeness of a system of eigen -

nonselfadjoint operators close to normal ones . Doklady Akad . Nauk SSSR 115 ,

207 – 210 ( 1957 ) . ( Russian ) Math . Rev . 20 # 1227 , 205 ( 1959 ) . 2 . On the ...

On the completeness of a system of eigen -

**elements**and adjoined**elements**ofnonselfadjoint operators close to normal ones . Doklady Akad . Nauk SSSR 115 ,

207 – 210 ( 1957 ) . ( Russian ) Math . Rev . 20 # 1227 , 205 ( 1959 ) . 2 . On the ...

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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 formal formula given gives Hence Hilbert space hypothesis identity inequality integral invariant inverse Lemma limit linear linear operator manifold Math Moreover multiplicity norm 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