## Linear Operators: Spectral theory |

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Page 1378

Pis a matrix measure { ê is } , i , i 1 , k of

Pis a matrix measure { ê is } , i , i 1 , k of

**Theorem**23 is unique , and = Pij , i , j = 1 , ... , k ; Pis = 0 , if i > k or ; > k . ; 0 k Proof . Suppose that 01 , ... , 07 is a determining set for T. Then it is evident from**Theorem**...Page 1379

a { is } is the matrix measure of

a { is } is the matrix measure of

**Theorem**23 , the values Pij ( e ) are uniquely determined for each e C N. Since 1 is the union of a sequence of neighborhoods of the same type as N , the uniqueness of { ộis } follows immediately .Page 1904

IV.15 Alexandroff

IV.15 Alexandroff

**theorem**on gence of measures , IV.9.15 ( 316 ) Arzela**theorem**continuous limits , IV.6.11 ( 268 ) Banach**theorem**for operators into Egoroff**theorem**on a.e. and y - uniform convergence , I11.6.12 ( 149 ) Fatou**theorem**...### What people are saying - Write a review

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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 given Hence Hilbert space identity independent indices inequality integral interval Lemma limit linear mapping Math matrix measure multiplicity Nauk 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