## Linear Operators: Spectral theory |

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Page 1218

Let u be a finite positive regular measure on the Borel sets of a topological space

R. Then , for every B - space valued

0 there is a Borel set o in R with M ( o ) < ε and such that the restriction of f to ...

Let u be a finite positive regular measure on the Borel sets of a topological space

R. Then , for every B - space valued

**u**-**measurable**function f on R and every e >0 there is a Borel set o in R with M ( o ) < ε and such that the restriction of f to ...

Page 1221

Thus om is the intersection of a sequence of measurable sets , and it follows that

Om is

proof of the theorem , suppose that the functions Wi ( : , ) , ... , W , ( :, 2 ) are not ...

Thus om is the intersection of a sequence of measurable sets , and it follows that

Om is

**u**-**measurable**, completing the proof of statement ( i ) . To complete theproof of the theorem , suppose that the functions Wi ( : , ) , ... , W , ( :, 2 ) are not ...

Page 1341

Let { Mij } be a positive matrix measure whose elements are continuous with

respect to a positive o - finite measure u . If { mij } is the matrix of densities of Hij

with respect to jl , then there exist nonnegative

...

Let { Mij } be a positive matrix measure whose elements are continuous with

respect to a positive o - finite measure u . If { mij } is the matrix of densities of Hij

with respect to jl , then there exist nonnegative

**u**-**measurable**functions ( i , i = 1 ,...

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### Contents

BAlgebras | 859 |

Bounded Normal Operators in Hilbert Space | 887 |

Miscellaneous Applications | 937 |

Copyright | |

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additive Akad algebra Amer analytic assume Banach spaces basis belongs Borel boundary conditions boundary values bounded called clear closed closure coefficients compact complex Consequently constant contains continuous converges Corollary corresponding defined Definition denote dense determined domain eigenvalues element equal equation essential spectrum evident Exercise exists extension finite follows formal differential operator formula function function f given Hence Hilbert space identity independent indices inequality integral interval Lemma limit linear mapping Math matrix measure multiplicity neighborhood norm obtained partial positive preceding present problem projection proof properties prove range regular remark representation respectively restriction result Russian satisfies seen sequence singular solution spectral square-integrable statement subset subspace sufficiently Suppose symmetric Theorem theory topology transform unique vanishes vector zero