## Linear Operators: Spectral operators |

### From inside the book

Results 1-3 of 98

Page 1951

Q.E.D 3

0 4 5. Proof. By

ideal in B(X) and so the present

Q.E.D 3

**Corollary**. If T is compact, then so are S, N, and every projection E(a) with0 4 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

5 (respectively SA0 =NA0 = E(a)A0 = 0i/0^5). 7

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

6

**Corollary**. // A0T = 0 (respectively TA0 = 0), then A0S = A0N = A0E(a) = 0 if 0 $5 (respectively SA0 =NA0 = E(a)A0 = 0i/0^5). 7

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

Page 2192

and completes the proof of the lemma. Q.E.D. 12

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

.

and completes the proof of the lemma. Q.E.D. 12

**Corollary**. Let 91 be an algebraof operators in a weakly complete B-space X. Suppose that 91 is topologically

and algebraically isomorphic to some B-algebra of bounded continuous functions

.

### What people are saying - Write a review

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

### Contents

SPECTRAL OPERATORS | 1924 |

Spectra Operators | 1925 |

Terminology and Preliminary Notions | 1928 |

Copyright | |

47 other sections not shown

### Other editions - View all

### Common terms and phrases

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