## 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 ( ayy

) 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 ( ayy

) has , for its

**elements**, the operators Qi , 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

Just as was the case with eBIS , * ) the

equivalence classes where two matrices À and B are equivalent if Â ( 8 ) = ( 8 ) B

for e - almost all 8 in S . For a given matrix Â = ( Quy ) in ŴP we shall use the

symbol feÂ ...

Just as was the case with eBIS , * ) the

**elements**of the algebra û P areequivalence classes where two matrices À and B are equivalent if Â ( 8 ) = ( 8 ) B

for e - almost all 8 in S . For a given matrix Â = ( Quy ) in ŴP we shall use the

symbol feÂ ...

Page 2512

( Russian . Armenian and English summaries ) Math . Rev . 34 # 8180 , 1504 (

1967 ) . Allahverdiev , Dž . È . 1 . On the completeness of a system of eigen -

ones .

( Russian . Armenian and English summaries ) Math . Rev . 34 # 8180 , 1504 (

1967 ) . Allahverdiev , Dž . È . 1 . On the completeness of a system of eigen -

**elements**and adjoined**elements**of nonselfadjoint operators close to normalones .

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### Contents

SPECTRAL OPERATORS | 1924 |

Introduction | 1927 |

Terminology and Preliminary Notions | 1929 |

Copyright | |

28 other sections not shown

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### Common terms and phrases

adjoint operator Amer analytic apply arbitrary assumed B-space Banach space belongs Boolean algebra Borel set boundary conditions bounded bounded operator Chapter clear closed commuting compact complex constant contains continuous converges Corollary corresponding countably additive defined Definition denote dense determined differential operator domain elements equation equivalent established exists extension fact finite follows formal formula given gives Hence Hilbert space hypothesis identity inequality integral invariant inverse Lemma limit linear operator Math Moreover multiplicity norm perturbation plane positive preceding present problem projections PROOF properties prove range resolution resolvent restriction Russian satisfies scalar type seen sequence shown shows similar solution spectral measure spectral operator spectrum subset sufficiently Suppose Theorem theory topology unbounded uniformly unique valued vector zero