## Linear Operators, Part 1 |

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Page 72

11 ) is a

: Given a Cauchy sequence in X / 3 , define a subsequence for which Xx - Xk + 1

+ 31 < 2 - k , k = 1 , 2 , . . . , and show that a Cauchy sequence in X can be ...

11 ) is a

**B**-**space**( or an F - space ) with the metric \ x + 31 = inf ( x + 2 . zez ( Hint: Given a Cauchy sequence in X / 3 , define a subsequence for which Xx - Xk + 1

+ 31 < 2 - k , k = 1 , 2 , . . . , and show that a Cauchy sequence in X can be ...

Page 89

In the definitions of F - and

their metric topology . ... Then X is isomorphic and isometric with a dense linear

subspace of an F - space X . The space X is uniquely determined up to isometric

...

In the definitions of F - and

**B**-**spaces**, we required the spaces to be complete intheir metric topology . ... Then X is isomorphic and isometric with a dense linear

subspace of an F - space X . The space X is uniquely determined up to isometric

...

Page 398

Let S be a Stone space and X = C ( S ) the real continuous functions .

Grothendieck [ 4 ; p . 168 ] showed that every X - convergent sequence in X * is

actually X * * - convergent , and that if Y is a separable

operator in B ( X ...

Let S be a Stone space and X = C ( S ) the real continuous functions .

Grothendieck [ 4 ; p . 168 ] showed that every X - convergent sequence in X * is

actually X * * - convergent , and that if Y is a separable

**B**-**space**, then anyoperator in B ( X ...

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### Contents

Preliminary Concepts | 1 |

B Topological Preliminaries | 10 |

Algebraic Preliminaries | 34 |

Copyright | |

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### Common terms and phrases

Akad 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 isomorphism Lebesgue Lemma limit linear functional linear operator linear space mapping Math meaning measure space metric 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