## 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 1945

Let L be the

f in L which are bilinear , Hermitian symmetric , and have f ( x , x ) 2 0 for all x in H

. Let L be given its weak product topology so that , by definition , the sets { f \ fe ...

Let L be the

**linear space**of all scalar functions on H x H and let P consist of thosef in L which are bilinear , Hermitian symmetric , and have f ( x , x ) 2 0 for all x in H

. Let L be given its weak product topology so that , by definition , the sets { f \ fe ...

Page 2068

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

Theodore Schwartz. For an operator ... We shall give some examples of such

algebras A . by specifying various choices for the

the ...

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

Theodore Schwartz. For an operator ... We shall give some examples of such

algebras A . by specifying various choices for the

**linear space**Lo . It is clear thatthe ...

Page 2096

A version of the canonical reduction for everywhere defined spectral operators in

a locally convex

quasicomplete and barreled . See below for remarks concerning the extension ...

A version of the canonical reduction for everywhere defined spectral operators in

a locally convex

**linear space**was given by Ionescu Tulcea [ 3 ] when the space isquasicomplete and barreled . See below for remarks concerning the extension ...

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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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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