## Linear Operators: Spectral operators |

### From inside the book

Results 1-3 of 76

Page 2141

Thus we may pass without loss of generality from consideration of the sequence {

0m } to consideration of the sequence { 0m - 0 } ; that is , we may and shall

by ...

Thus we may pass without loss of generality from consideration of the sequence {

0m } to consideration of the sequence { 0m - 0 } ; that is , we may and shall

**assume**without loss of generality that o is void . Since Edom ) = E ( Om O ( T ) ) ,by ...

Page 2212

To prove ( ix ) it may be

we may and shall

— Ay it follows that T ( fz - y ) ( x - y ) = T ( f : ) x — T ( fyly , and consequently that T

...

To prove ( ix ) it may be

**assumed**that 0 , = Oy , for if z = E , x and w = E ... Hencewe may and shall

**assume**, in the proof of ( ix ) , that o = oy Since A ( x - y ) = Ax— Ay it follows that T ( fz - y ) ( x - y ) = T ( f : ) x — T ( fyly , and consequently that T

...

Page 2342

Nelson Dunford, Jacob T. Schwartz, William G. Bade, Robert Gardner Bartle.

being boundary values for 7 at 0 , B , + 1 , . . . , B2 , being boundary values for 7 at

1 . By the remark following formula ( 3 ) , it is no loss of generality to

...

Nelson Dunford, Jacob T. Schwartz, William G. Bade, Robert Gardner Bartle.

being boundary values for 7 at 0 , B , + 1 , . . . , B2 , being boundary values for 7 at

1 . By the remark following formula ( 3 ) , it is no loss of generality to

**assume**that...

### What people are saying - Write a review

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

### Contents

SPECTRAL OPERATORS | 1924 |

Spectral Operators | 1925 |

Terminology and Preliminary Notions | 1928 |

Copyright | |

31 other sections not shown

### Other editions - View all

### Common terms and phrases

adjoint operator analytic applications arbitrary assumed B-space Banach space belongs Boolean algebra Borel sets boundary bounded bounded operator Chapter clear closed commuting compact complex condition consider constant contained continuous converges Corollary corresponding countably additive defined Definition denote dense determined domain elements equation equivalent established example exists extension fact finite follows formula given gives Hence Hilbert space hypothesis identity inequality integral invariant inverse Lemma limit linear linear operator manifold Math Moreover multiplicity norm normal perturbation plane positive preceding present problem projections PROOF properties proved range regular resolution resolvent respectively restriction Russian satisfies scalar type seen sequence shown shows similar spectral measure spectral operator spectrum subset subspace sufficiently Suppose Theorem theory topology unbounded uniformly unique valued vector weakly zero