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

### From inside the book

Results 1-3 of 78

Page 2094

It follows from some results of Bade [ 4 ] ( see also XVII.2.1 and XVII.2.12 ) that if X

is a weakly complete B - space , then any prespectral operator is automatically

spectral , and so has a

] ...

It follows from some results of Bade [ 4 ] ( see also XVII.2.1 and XVII.2.12 ) that if X

is a weakly complete B - space , then any prespectral operator is automatically

spectral , and so has a

**unique**resolution of the identity . Berkson and Dowson [ 1] ...

Page 2143

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

Theodore Schwartz. 11 THEOREM ( A , B ) . Let T be a bounded linear operator

in the complex B - space X. Then there is a

...

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

Theodore Schwartz. 11 THEOREM ( A , B ) . Let T be a bounded linear operator

in the complex B - space X. Then there is a

**unique**spectral measure on the field...

Page 2265

Let D be a dense ideal in B and m be a function on D to cardinals such that m ( 0

) = 0 and m ( Va E. ) = Væm ( Ec ) for each family { Ex } $ D for which VaEge D.

Then there is a

Let D be a dense ideal in B and m be a function on D to cardinals such that m ( 0

) = 0 and m ( Va E. ) = Væm ( Ec ) for each family { Ex } $ D for which VaEge D.

Then there is a

**unique**multiplicity function on B which is an extension of m on D.### What people are saying - Write a review

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### Contents

SPECTRAL OPERATORS | 1924 |

Introduction | 1927 |

Terminology and Preliminary Notions | 1929 |

Copyright | |

47 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 defined Definition denote dense determined differential operator discrete domain elements equation equivalent established exists extension fact finite follows formal formula function 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