## Linear Operators: Spectral operators |

### From inside the book

Results 1-3 of 74

Page 2222

Then T is a scalar type spectral operator if and only if there exists a

such that If ( T ) | S Alf1 , fe R ( O ( T ) ) . 3 Let X be a reflexive B - space and Te B (

x ) and suppose that o ( T ) is an R - set . Then T is a scalar type spectral operator

...

Then T is a scalar type spectral operator if and only if there exists a

**constant**Asuch that If ( T ) | S Alf1 , fe R ( O ( T ) ) . 3 Let X be a reflexive B - space and Te B (

x ) and suppose that o ( T ) is an R - set . Then T is a scalar type spectral operator

...

Page 2439

Oki Ok , " Let us now note that there exists a positive absolute

that ( 31 ) 1W - aw ' | 2 clw – w ' ll for all 0 < « < l and all w , w ' e E . Indeed , if 0 is

the angle between w and w ' , it is clear that ( w – aw ' > 1 if 7 / 2 = 10 Ş TT , while

...

Oki Ok , " Let us now note that there exists a positive absolute

**constant**c suchthat ( 31 ) 1W - aw ' | 2 clw – w ' ll for all 0 < « < l and all w , w ' e E . Indeed , if 0 is

the angle between w and w ' , it is clear that ( w – aw ' > 1 if 7 / 2 = 10 Ş TT , while

...

Page 2441

This shows that there exists a finite absolute

+ 10l ) - n + 1 . Using this inequality and using ( 37 ) , we see that there exists a

finite

...

This shows that there exists a finite absolute

**constant**c ' such that I ( Q ) ] = c ' ( 1+ 10l ) - n + 1 . Using this inequality and using ( 37 ) , we see that there exists a

finite

**constant**M ” independent of ε such that ( 43 ) [ Parryn til en ry 09 + ( Lale 07...

### What people are saying - Write a review

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

### Other editions - View all

### Common terms and phrases

algebra of projections analytic apply arbitrary assumed B-space Banach space Boolean algebra Borel sets boundary conditions bounded bounded Borel bounded operator Chapter clear closure commuting compact complete consider constant contained converges Corollary corresponding countably additive defined Definition denote dense determined differential operator 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 positive preceding present problem projections PROOF properties prove range regular resolution resolvent respectively restriction Russian satisfies scalar type seen sequence shown shows spectral measure spectral operator spectrum strongly subset subspace sufficiently Suppose Theorem theory topology unbounded uniformly unique valued vector weakly zero