## 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 88

Page 2130

For an exposition of ordered topological vector

For an exposition of ordered topological vector

**spaces**, we refer the reader to the books of Day [ 12 ] , Kelley and ... If X is a real**B**-**space**which is ordered by < , let X ; = X 9 X and define : ( a + iB ) ( x , y ] = [ ox - By ...Page 2193

Q.E.D. The preceding corollary is not true if the Hilbert

Q.E.D. The preceding corollary is not true if the Hilbert

**space**is replaced by an arbitrary**B**-**space**, for it has been shown by Kakutani [ 15 ] that the sum of two commuting scalar type spectral operators in a**space**of continuous ...Page 2484

( c ) Show that +00 8 - o

( c ) Show that +00 8 - o

**B**( 8,0 )**B**( 8,0 ) lim do = 90 do FiTA ( 8,8 ) . 8 + 0 +/- 8-0 Eie Let H be a Hilbert**space**, and let**B**( H ) be the**B**-**space**of all bounded operators in H. Let C ( s , t ) be a**B**...### 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