## Linear Operators, Part 1 |

### From inside the book

Results 1-3 of 81

Page 88

Nelson Dunford, Jacob T. Schwartz. 1x1 = p ( x ) + p ( - x ) , then this condition is

Ingleton [ 1 ] has given conditions for the Hahn - Banach theorem to hold when ...

Nelson Dunford, Jacob T. Schwartz. 1x1 = p ( x ) + p ( - x ) , then this condition is

**sufficient**. Bonsall [ 1 ] showed that the separability condition cannot be dropped .Ingleton [ 1 ] has given conditions for the Hahn - Banach theorem to hold when ...

Page 383

30 – 36 ] independently demonstrated that uniform convergence is

assure the continuity of the limit function . ( It is interesting that Weierstrass [ 1 ; p .

67 , 70 ] had employed this notion of convergence in some unpublished ...

30 – 36 ] independently demonstrated that uniform convergence is

**sufficient**toassure the continuity of the limit function . ( It is interesting that Weierstrass [ 1 ; p .

67 , 70 ] had employed this notion of convergence in some unpublished ...

Page 472

Smulian [ 7 ] obtains two interesting necessary and

differentiability of the norm . THEOREM . In order that the norm is strongly

differentiable at a point æ in a B - space X , it is necessary and

every ...

Smulian [ 7 ] obtains two interesting necessary and

**sufficient**conditions for strongdifferentiability of the norm . THEOREM . In order that the norm is strongly

differentiable at a point æ in a B - space X , it is necessary and

**sufficient**thatevery ...

### What people are saying - Write a review

We haven't found any reviews in the usual places.

### Contents

Preliminary Concepts | 1 |

B Topological Preliminaries | 10 |

Algebraic Preliminaries | 34 |

Copyright | |

25 other sections not shown

### Other editions - View all

### 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 obtained 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