## Linear Operators, Part 2 |

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Page 1378

نم matrix measure { fus } , i , j = 1 , ... , k of

... , k ; Pis = 0 , if i > k or ; > k . Proof . Suppose that 01 , ... , 0x is a determining set

for T. Then it is evident from

نم matrix measure { fus } , i , j = 1 , ... , k of

**Theorem**23 is unique , and Pij , i , j = 1 ,... , k ; Pis = 0 , if i > k or ; > k . Proof . Suppose that 01 , ... , 0x is a determining set

for T. Then it is evident from

**Theorem**23 that if we define { Pus } , i , = 1 , ... , n ...Page 1379

Nelson Dunford, Jacob T. Schwartz, William G. Bade, Robert G. Bartle. { êuj } is

the matrix measure of

each e C N. Since 1 is the union of a sequence of neighborhoods of the same ...

Nelson Dunford, Jacob T. Schwartz, William G. Bade, Robert G. Bartle. { êuj } is

the matrix measure of

**Theorem**23 , the values Pijle ) are uniquely determined foreach e C N. Since 1 is the union of a sequence of neighborhoods of the same ...

Page 1904

IV.15 Alexandroff

continuous limits , IV.6.11 ( 268 ) Banach

limits ...

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 u - uniform convergence , III.6.12 ( 149 ) Fatou**theorem**onlimits ...

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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