## Linear Operators: General theory |

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Page 72

11) is a

Cauchy sequence in X/3> define a subsequence for which \xk— xk+1-\-Q\ < 2~*>

k = 1, 2, . . ., and show that a Cauchy sequence in 3c can be chosen which ...

11) is a

**B**-**space**(or an /-'-space) with the metric |.i'+3l = inf \x+z\. "8 (Hint: Given aCauchy sequence in X/3> define a subsequence for which \xk— xk+1-\-Q\ < 2~*>

k = 1, 2, . . ., and show that a Cauchy sequence in 3c can be chosen which ...

Page 89

It will be fundamental in the discussion of B-algebras. Completian of spaces. In

the definitions of F- and

metric topology. Occasionally it is necessary to consider metric linear spaces ...

It will be fundamental in the discussion of B-algebras. Completian of spaces. In

the definitions of F- and

**B**-**spaces**, we required the spaces to be complete in theirmetric topology. Occasionally it is necessary to consider metric linear spaces ...

Page 398

Let S be a Stone space and 3c = C(S) the real continuous functions.

Grothendieck [4; p. 168] showed that every 3E-convergent sequence in S* is

actually 3£**-convergent, and that if ?) is a separable

in B(£, 'J)) is ...

Let S be a Stone space and 3c = C(S) the real continuous functions.

Grothendieck [4; p. 168] showed that every 3E-convergent sequence in S* is

actually 3£**-convergent, and that if ?) is a separable

**B**-**space**, then any operatorin B(£, 'J)) is ...

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### Contents

Preliminary Concepts | 1 |

B Topological Preliminaries | 10 |

Algebraic Preliminaries 84 | 34 |

Copyright | |

44 other sections not shown

### 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

Acad additive set function algebra Amer analytic arbitrary B-space ba(S Banach spaces Borel sets ca(S Cauchy sequence closed unit sphere compact Hausdorff space compact operator complex numbers contains continuous functions convex set Corollary countably additive Definition denote dense differential equations Doklady Akad Duke Math element equivalent exists finite dimensional function defined function f Hausdorff space Hence Hilbert space homeomorphism implies inequality integral interval isometric isomorphism Lemma linear map linear operator linear topological space LP(S measurable functions measure space metric space Nauk SSSR N. S. neighborhood non-negative normed linear space null set open set operator topology positive measure space Proc properties proved real numbers reflexive Riesz Russian scalar semi-group sequentially compact Show simple functions subset subspace Suppose theory TM(S topological space Trans valued function Vber vector space weak topology weakly compact weakly sequentially compact zero