## Linear operators: Spectral operators |

### From inside the book

Results 1-3 of 90

Page 1951

Q.E.D 3

0$5. Proof. By

ideal in B( X) and so the present

Q.E.D 3

**Corollary**. // T is compact, then so are S, N, and every projection E(a) with0$5. Proof. By

**Corollary**VI. 5. 5 the compact operators form a closed two- sidedideal in B( X) and so the present

**corollary**is immediate. Q.E.D. 4**Corollary**.Page 1952

6

respectively SA0=NA0= E(o)A0 = 0 if 0 £ a). 7

finite type if and only if it is annihilated by some power of its radical part. Proof.

6

**Corollary**. If A0 T = 0 {respectively TA0 = 0), then A0S = A0N = A0E(a) =0if0$d (respectively SA0=NA0= E(o)A0 = 0 if 0 £ a). 7

**Corollary**. A spectral operator is offinite type if and only if it is annihilated by some power of its radical part. Proof.

Page 2192

Q.E.D. 12

space X. Suppose that 91 is topologically and algebraically isomorphic to some B

-algebra of bounded continuous functions. Then every operator in 'His a scalar ...

Q.E.D. 12

**Corollary**. Let 31 be an algebra of operators in a weakly complete B -space X. Suppose that 91 is topologically and algebraically isomorphic to some B

-algebra of bounded continuous functions. Then every operator in 'His a scalar ...

### 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 | |

47 other sections not shown

### Other editions - View all

### Common terms and phrases

adjoint operator algebra of projections Amer analytic arbitrary asymptotic B-space Banach space Boolean algebra Borel sets boundary conditions bounded Borel function bounded linear operator bounded operator commuting compact complex numbers complex plane constant contains continuous functions converges Corollary countably additive Definition denote dense differential operator disjoint Doklady Akad domain eigenvalues elements equation exists finite number Foias follows from Lemma follows from Theorem formal differential operator formula Hence Hilbert space hypothesis identity inequality inverse Lebesgue Math matrix measurable functions multiplicity Nauk SSSR norm normal operators operators in Hilbert perturbation polynomial Proof properties prove quasi-nilpotent restriction Russian satisfies scalar operator scalar type operator scalar type spectral Section semi-group sequence shows spectral measure spectral operator spectral theory spectrum strong operator topology subset Suppose trace class type spectral operator unbounded uniformly bounded unique vector weakly complete zero