## Linear Operators: Spectral operators |

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Page 2512

Nelson Dunford, Jacob T. Schwartz, William G. Bade, Robert Gardner Bartle.

REFERENCES Adamjan , V . M . , and Arov , D . Z . 1 . On a class of scattering

operators and characteristic operator - functions of contractions . Doklady

Nelson Dunford, Jacob T. Schwartz, William G. Bade, Robert Gardner Bartle.

REFERENCES Adamjan , V . M . , and Arov , D . Z . 1 . On a class of scattering

operators and characteristic operator - functions of contractions . Doklady

**Akad**.Page 2549

( Russian ) Math . Rev . 33 # 4680 , 792 ( 1967 ) . 6 . Expansion in characteristic

functions of a non - selfadjoint differential operator with spectral singularities .

Doklady

Dokl .

( Russian ) Math . Rev . 33 # 4680 , 792 ( 1967 ) . 6 . Expansion in characteristic

functions of a non - selfadjoint differential operator with spectral singularities .

Doklady

**Akad**. Nauk SSSR 149 , 256 – 259 ( 1963 ) . ( Russian ) Soviet Math .Dokl .

Page 2552

The root - vector expansion of a weakly perturbed self - adjoint operator . Doklady

361 ( 1964 ) . Eigenvalues and singular values of the sum and product of linear ...

The root - vector expansion of a weakly perturbed self - adjoint operator . Doklady

**Akad**. Nauk SSSR 142 , 538 – 541 ( 1962 ) . ( Russian ) Math . Rev . 27 # 1837 ,361 ( 1964 ) . Eigenvalues and singular values of the sum and product of linear ...

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### Contents

SPECTRAL OPERATORS | 1924 |

Spectral Operators | 1925 |

Terminology and Preliminary Notions | 1928 |

Copyright | |

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### Common terms and phrases

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