## Linear Operators: Spectral theory |

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Page 891

scalar

chapter we shall only integrate ... It is assumed that E is

i.e., there is a constant K such that for every pair 6, a of disjoint

...

scalar

**function**f with respect to the operator valued**set function**E. In the presentchapter we shall only integrate ... It is assumed that E is

**additive**and bounded,i.e., there is a constant K such that for every pair 6, a of disjoint

**sets**in 2, (vii) E(6...

Page 958

Hence if e1 and ea are disjoint then op(ei U ex) = E(ei U ex)y(ei U ea) = [E(e1)+E

(eg)]"p(ei U ea) = E(e)y(ei U ea)+E(es)w(ei U ea) = p(e1)+"p(ee), so that the

vector valued

Hence if e1 and ea are disjoint then op(ei U ex) = E(ei U ex)y(ei U ea) = [E(e1)+E

(eg)]"p(ei U ea) = E(e)y(ei U ea)+E(es)w(ei U ea) = p(e1)+"p(ee), so that the

vector valued

**set function**p is**additive**on 30. Therefore, if ei nea = b, the**set****function**...Page 1899

(See Continuous set function and Set function) space of, additional properties, IV.

15 (378) definition, IV.2.22 (242) ... (392) study of, IV.12.3 (338) Absolute

convergence, in a B-space, (98) Accumulation, point of, I.4.1 (10)

(See Continuous set function and Set function) space of, additional properties, IV.

15 (378) definition, IV.2.22 (242) ... (392) study of, IV.12.3 (338) Absolute

convergence, in a B-space, (98) Accumulation, point of, I.4.1 (10)

**Additive set****function**.### What people are saying - Write a review

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### Contents

SPECTRAL THEORY | 858 |

Bounded Normal Operators in Hilbert Space | 887 |

Miscellaneous Applications | 937 |

Copyright | |

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