## Linear Operators: Spectral operators |

### From inside the book

Results 1-3 of 52

Page 1978

To illustrate more clearly the relationship between Theorem 6 and the well known

result for self adjoint operators , we observe that a self adjoint operator or , more

generally , a

To illustrate more clearly the relationship between Theorem 6 and the well known

result for self adjoint operators , we observe that a self adjoint operator or , more

generally , a

**normal**operator in AP is a spectral operator . For if A is a**normal**...Page 2005

( 56 ) where h is Hilbert ' s singular integral ( 34 ) , is an operator in A2 which is

not self adjoint , and not

choices of a and b , a spectral operator . To see this , equation ( 35 ) shows that

the ...

( 56 ) where h is Hilbert ' s singular integral ( 34 ) , is an operator in A2 which is

not self adjoint , and not

**normal**unless i ( a – b ) is self adjoint but is , for manychoices of a and b , a spectral operator . To see this , equation ( 35 ) shows that

the ...

Page 2516

The spectral theorem for

486 ( 1965 ) . 2 . The spectral theorem for unbounded

. Math . 19 , 391 - 406 ( 1966 ) . 3 . Extreme eigenvectors of a

The spectral theorem for

**normal**operators . J . London Math . Soc . 40 , 478 –486 ( 1965 ) . 2 . The spectral theorem for unbounded

**normal**operators . Pacific J. Math . 19 , 391 - 406 ( 1966 ) . 3 . Extreme eigenvectors of a

**normal**operator .### 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