## Linear Operators: Spectral operators |

### From inside the book

Results 1-3 of 83

Page 2242

T = T ( f ) in the sense of

unbounded spectral operator of scalar type . The projection valued measure E is

said to be the resolution of the identity for T . 13 LEMMA . An unbounded spectral

...

T = T ( f ) in the sense of

**Definition**10 , where f ( z ) = , then T is said to be anunbounded spectral operator of scalar type . The projection valued measure E is

said to be the resolution of the identity for T . 13 LEMMA . An unbounded spectral

...

Page 2590

6 ( 2501 ) , ( 2507 ) Quasi - nilpotent operator ,

spectrum of , XV . 4 . 3 ( 1939 ) Quasi - nilpotent part of a spectral operator ,

XV . 4 .

6 ( 2501 ) , ( 2507 ) Quasi - nilpotent operator ,

**definition**of , XV . 4 . 2 ( 1938 )spectrum of , XV . 4 . 3 ( 1939 ) Quasi - nilpotent part of a spectral operator ,

**definition**of , XV . 4 . 6 ( 1941 ) Radical part of a spectral operator ,**definition**of ,XV . 4 .

Page 2591

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

additive , XV . 2 ( 1930 ) , XV . 2 . 3 ( 1930 ) , XV . 2 . 4 ( 1931 )

. 1 ( 1929 ) integral with respect to , XV . 2 ( 1929 ) Spectral operator , adjoint of ...

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

additive , XV . 2 ( 1930 ) , XV . 2 . 3 ( 1930 ) , XV . 2 . 4 ( 1931 )

**definition**of , XV . 2. 1 ( 1929 ) integral with respect to , XV . 2 ( 1929 ) Spectral operator , adjoint of ...

### 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