## Linear Operators, Part 1 |

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Results 1-3 of 67

Page 237

Each of these spaces is studied in an attempt to solve the eight

below . The results of these studies are presented in tabular form in Section 14 . 1

Each of these spaces is studied in an attempt to solve the eight

**problems**listedbelow . The results of these studies are presented in tabular form in Section 14 . 1

**Problem**. What is an analytical representation of the conjugate space X * of the ...Page 613

A corresponding

valued functions defined on the range t = 0 , which satisfy the equations ( i ) T ( t +

u ) = T ( t ) T ( u ) , T ( 0 ) = 1 , t , u 20 . An operator valued function T ( t ) satisfying

...

A corresponding

**problem**is to determine the most general continuous operatorvalued functions defined on the range t = 0 , which satisfy the equations ( i ) T ( t +

u ) = T ( t ) T ( u ) , T ( 0 ) = 1 , t , u 20 . An operator valued function T ( t ) satisfying

...

Page 658

Thus , the mathematician is led to the

limit ( iii ) exists . The next four sections are devoted to a study of this

various of its generalizations which arise in the theory of stochastic processes .

Thus , the mathematician is led to the

**problem**of determining whether or not thelimit ( iii ) exists . The next four sections are devoted to a study of this

**problem**andvarious of its generalizations which arise in the theory of stochastic processes .

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### Contents

Preliminary Concepts | 1 |

B Topological Preliminaries | 10 |

Algebraic Preliminaries | 34 |

Copyright | |

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### Other editions - View all

Linear Operators, Part 1 Nelson Dunford,Jacob T. Schwartz,William G. Bade,Robert G. Bartle Snippet view - 1958 |

### Common terms and phrases

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