## Linear operators: Spectral operators |

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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 ...

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### Contents

SPECTRAL OPERATORS | 1924 |

Spectral Operators | 1925 |

Terminology and Preliminary Notions | 1928 |

Copyright | |

47 other sections not shown

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