## Linear Operators: General theory |

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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 2 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 2 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 766

On the moment

270 ( 1932 ) . 9 . Convergence of sequences of linear operations . Bull . Amer .

Math . Soc . 28 , 53 - 58 ( 1922 ) . Hildebrandt , T . H . , and Graves , L . M . 1 .

On the moment

**problem**for a finite interval . Bull . Amer . Math . Soc . 38 , 269 –270 ( 1932 ) . 9 . Convergence of sequences of linear operations . Bull . Amer .

Math . Soc . 28 , 53 - 58 ( 1922 ) . Hildebrandt , T . H . , and Graves , L . M . 1 .

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### Contents

Metric Spaces | 19 |

Convergence and Uniform Convergence of Generalized | 26 |

Exercises | 33 |

Copyright | |

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Acad algebra Amer analytic applied arbitrary assumed B-space Banach Banach spaces bounded called clear closed compact complex 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