## 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 linear space of all scalar functions on H X H and let P consist of those f in L which are bilinear , Hermitian

Let L be the linear space of all scalar functions on H X H and let P consist of those 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 ...Page 2308

On the other hand , if is complex then , since ( T. ( T ) ) is

On the other hand , if is complex then , since ( T. ( T ) ) is

**symmetric**by Lemma XII.4.8 , it follows from Lemma XII.2.1 that f = 0 . This completes the proof of the lemma . Q.E.D. 2 COROLLARY . Lett be a formally**symmetric**formal ...Page 2478

Suppose that V , is a

Suppose that V , is a

**symmetric**operator in H , that D ( V . ) 2 D ( H4 ) , that the operator V. ( il - H2 ) -1 is compact , and that for each bounded interval e of the real axis the operator ( il – H4 ) -1V4E4 ( e ) is of trace class .### 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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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