## Linear Operators: Spectral Theory : Self Adjoint Operators in Hilbert Space, Volume 2 |

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Page 2130

Spectral Theory : Self Adjoint Operators in Hilbert Space Nelson Dunford, Jacob

Theodore Schwartz. K = { x € V10 x } is called the

to 5 ) ; it is easy to see that K satisfies ( i ) K + K SK , ( ii ) AK ĒK for all le R , 20 ...

Spectral Theory : Self Adjoint Operators in Hilbert Space Nelson Dunford, Jacob

Theodore Schwartz. K = { x € V10 x } is called the

**positive**cone of V ( with respectto 5 ) ; it is easy to see that K satisfies ( i ) K + K SK , ( ii ) AK ĒK for all le R , 20 ...

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

A remark on the Volterra operator . J . Math . Anal . Appl . 12 , 244 – 246 ( 1965 ) .

3 . Invariant subspaces and unstarred operator algebras . Pacific J . Math . 17 ,

511 - 517 ( 1966 ) . Sasser , D . W . 1 . Quasi -

...

A remark on the Volterra operator . J . Math . Anal . Appl . 12 , 244 – 246 ( 1965 ) .

3 . Invariant subspaces and unstarred operator algebras . Pacific J . Math . 17 ,

511 - 517 ( 1966 ) . Sasser , D . W . 1 . Quasi -

**positive**operators . Pacific J . Math...

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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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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