## Linear Operators: General theory |

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Page 195

Indeed , according to Tonelli ' s theorem , both these

that the product of measures is commutative . ) Generalizing this statement , and

...

Indeed , according to Tonelli ' s theorem , both these

**integrals**are equal to the**integral**off with respect to the product measure ( and we have already remarkedthat the product of measures is commutative . ) Generalizing this statement , and

...

Page 227

Lett be analytic in V - A . Then the second form of Cauchy ' s

states : If we agree to orient the Jordan ... and is independent of any particular

choice of the neighborhood U of A . In other words , the

...

Lett be analytic in V - A . Then the second form of Cauchy ' s

**integral**theoremstates : If we agree to orient the Jordan ... and is independent of any particular

choice of the neighborhood U of A . In other words , the

**integrals**SB and SB , are...

Page 232

The possibility of extending the

Graves [ 3 ] , who discussed and applied the Riemann

Lebesgue type was constructed by Bochner [ 2 ] . The Cauchy sequence method

of ...

The possibility of extending the

**integral**to this realm was recognized by L . M .Graves [ 3 ] , who discussed and applied the Riemann

**integral**. A theory of theLebesgue type was constructed by Bochner [ 2 ] . The Cauchy sequence method

of ...

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### Contents

Preliminary Concepts | 1 |

B Topological Preliminaries | 10 |

Algebraic Preliminaries | 34 |

Copyright | |

31 other sections not shown

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### Common terms and phrases

algebra Amer analytic applied arbitrary assumed B-space Banach spaces bounded called clear closed compact operator complex condition Consequently constant contains continuous functions converges convex convex set Corollary countably additive defined DEFINITION denote dense determined differential dimensional disjoint domain element equation equivalent everywhere Exercise exists extension field finite follows formula function defined function f given Hence Hilbert space identity implies inequality integral interval Lebesgue Lemma limit linear functional linear operator linear space Math neighborhood norm operator operator topology problem projection PROOF properties proved range reflexive representation respect satisfies scalar seen semi-group separable sequence set function Show shown statement subset subspace sufficient Suppose Theorem theory topology u-measurable uniform uniformly unique unit sphere valued vector weak weakly compact zero