## 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 |

### From inside the book

Results 1-3 of 36

Page 1961

... i # j , ( 7 ) The symbol I will be used for the

in B ( H ) , that is , the identity operator in H . 181 = 1 XV . 9 1961 THE

ALGEBRAS UP AND ØP.

... i # j , ( 7 ) The symbol I will be used for the

**unit**in. = e , i = j , where e is the**unit**in B ( H ) , that is , the identity operator in H . 181 = 1 XV . 9 1961 THE

ALGEBRAS UP AND ØP.

Page 1964

... ( s ) for e - almost all s in S . The space eBIS , 2 ) , with the natural algebraic

operations , is clearly a commutative B * - algebra with

. The symbol û will be used for a B * - subalgebra of eBIS , 2 ) with the same

ê .

... ( s ) for e - almost all s in S . The space eBIS , 2 ) , with the natural algebraic

operations , is clearly a commutative B * - algebra with

**unit**ê ( s ) = 1 for all s in S. The symbol û will be used for a B * - subalgebra of eBIS , 2 ) with the same

**unit**ê .

Page 2509

operators – ( d / dx ) 2 and - ( d / dx ) 2 + V ( x ) , where V is integrable ,

nonnegative , and bounded , have continuous spectra covering the

and , under slightly stronger hypotheses , that these spectra are absolutely

continuous .

operators – ( d / dx ) 2 and - ( d / dx ) 2 + V ( x ) , where V is integrable ,

nonnegative , and bounded , have continuous spectra covering the

**unit**circle ,and , under slightly stronger hypotheses , that these spectra are absolutely

continuous .

### What people are saying - Write a review

We haven't found any reviews in the usual places.

### Contents

SPECTRAL OPERATORS | 1924 |

Introduction | 1927 |

Terminology and Preliminary Notions | 1929 |

Copyright | |

47 other sections not shown

### Other editions - View all

### 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