## 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 2130

... [by] Nelson Dunford and Jacob T. Schwartz, with the Assistance of William G.

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

Robert G. Bartle L. Bers, J. J. Stoker. K = { x € V10 x } is called the

...

... [by] Nelson Dunford and Jacob T. Schwartz, with the Assistance of William G.

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

Robert G. Bartle L. Bers, J. J. Stoker. K = { x € V10 x } is called the

**positive**cone of...

Page 2500

... and where K ( a ) is

more generally if there exists a Hermitian operator T , with finite range such that

H2 - H2 + To is

...

... and where K ( a ) is

**positive**for almost all , if H , - H , is a**positive**operator , ormore generally if there exists a Hermitian operator T , with finite range such that

H2 - H2 + To is

**positive**. Similar results are proved by Birman and Krein for a pair...

Page 2564

Quasi -

Sawashima , I . ( see also Niiro , F . ) 1 . Some counter examples in the theory of

1964 ) . 2 .

Quasi -

**positive**operators . Pacific J . Math . 14 , 1029 – 1037 ( 1964 ) .Sawashima , I . ( see also Niiro , F . ) 1 . Some counter examples in the theory of

**positive**operators . Sci . Papers College Gen . Ed . Univ . Tokyo 14 , 181 - 182 (1964 ) . 2 .

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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