## 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

those f in L which are bilinear , Hermitian symmetric , and have f ( x , x ) 20 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 ofthose f in L which are bilinear , Hermitian symmetric , and have f ( x , x ) 20 for all

x in H . Let L be given its weak product topology so that , by definition , the sets { f

\ fe ...

Page 2068

For an operator a in A , the function â is continuous on the compact space S , and

so its non - vanishing is equivalent to the existence of ... We shall give some

examples of such algebras A , by specifying various choices for the

Lo .

For an operator a in A , the function â is continuous on the compact space S , and

so its non - vanishing is equivalent to the existence of ... We shall give some

examples of such algebras A , by specifying various choices for the

**linear space**Lo .

Page 2096

The notion of subscalar operators and scalar extensions in B - spaces has been

pursued by Ionescu Tulcea [ 4 , 5 ] and ... A version of the canonical reduction for

everywhere defined spectral operators in a locally convex

The notion of subscalar operators and scalar extensions in B - spaces has been

pursued by Ionescu Tulcea [ 4 , 5 ] and ... A version of the canonical reduction for

everywhere defined spectral operators in a locally convex

**linear space**was ...### 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 countably additive defined Definition denote dense determined differential operator 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