## Linear Operators, Part 1 |

### From inside the book

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Page 177

Nelson Dunford, Jacob T. Schwartz. E C En may be

. A real valued set function can be represented as the difference of its positive

and negative variations ( 4.11 ) and so we may also

Nelson Dunford, Jacob T. Schwartz. E C En may be

**assumed**that 2 is real valued. A real valued set function can be represented as the difference of its positive

and negative variations ( 4.11 ) and so we may also

**assume**that 2 is positive .Page 278

Let H be an algebraic homomorphism of C ( S ) into C ( T ) , where S and T are

compact Hausdorff spaces . If the algebras C ( S ) and C ( T ) are over the field of

complex numbers , it is also

...

Let H be an algebraic homomorphism of C ( S ) into C ( T ) , where S and T are

compact Hausdorff spaces . If the algebras C ( S ) and C ( T ) are over the field of

complex numbers , it is also

**assumed**that HÌ = IIf . Then H is continuous and has...

Page 657

The problem may be formulated in abstract terms as follows : The momentary

state of a mechanical system is described by specifying a point in a " phase

space " S. The mechanical system is

The problem may be formulated in abstract terms as follows : The momentary

state of a mechanical system is described by specifying a point in a " phase

space " S. The mechanical system is

**assumed**to be governed by the classical ...### What people are saying - Write a review

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### Contents

Preliminary Concepts | 1 |

The VitaliHahnSaks Theorem and Spaces of Measures | 7 |

B Topological Preliminaries | 10 |

Copyright | |

87 other sections not shown

### Common terms and phrases

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