## 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 20 , 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 20 , 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 777

Sur une généralisation du théorème de Plancherel au cas des intégrales de

Fourier sur les groupes topologiques commutatifs . Doklady Akad . Nauk SSSR (

N . S . ) 30 , 484 - 488 ( 1941 ) . Infinite J - matrices and a matrix moment

.

Sur une généralisation du théorème de Plancherel au cas des intégrales de

Fourier sur les groupes topologiques commutatifs . Doklady Akad . Nauk SSSR (

N . S . ) 30 , 484 - 488 ( 1941 ) . Infinite J - matrices and a matrix moment

**problem**.

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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