## Linear Operators: General theory |

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Page 177

Nelson Dunford, Jacob T. Schwartz. may be

valued set function can be represented as the difference of its positive and

negative variations ( 4 . 11 ) and so we may also assume that a is positive . Let ,

then ...

Nelson Dunford, Jacob T. Schwartz. may be

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

negative variations ( 4 . 11 ) and so we may also assume that a is positive . Let ,

then ...

Page 278

Let II 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

has ...

Let II 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 Hs = Hlf . Then H is continuous andhas ...

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

Special Spaces | 237 |

Convex Sets and Weak Topologies | 409 |

General Spectral Theory | 555 |

Copyright | |

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Acad algebra Amer analytic applied arbitrary assumed B-space Banach Banach spaces bounded called clear closed compact complex Consequently contains continuous functions converges convex Corollary countably additive defined DEFINITION denote dense determined differential disjoint Doklady Akad domain elements equation equivalent everywhere Exercise exists extension field finite follows function defined function f given Hence Hilbert space implies inequality integral interval isomorphism Lebesgue Lemma limit linear functional linear operator linear space mapping Math mean measure space metric space neighborhood norm operator positive problem Proc PROOF properties proved range regular respect Russian satisfies scalar seen semi-group separable sequence set function Show shown sphere statement subset Suppose Theorem theory topological space topology transformations u-integrable u-measurable uniformly union unique unit valued vector weak zero