## Linear Operators, Part 1 |

### From inside the book

Results 1-3 of 63

Page 485

Since the closed unit

Lemma 7 and Lemma 1.5.7 that T * S * is ... If S , S ** are the closed unit

in X , X ** , respectively , and if x is the natural embedding of X into X ** , then by ...

Since the closed unit

**sphere**S * of Y * is Y - compact ( V.4.2 ) , it follows fromLemma 7 and Lemma 1.5.7 that T * S * is ... If S , S ** are the closed unit

**spheres**in X , X ** , respectively , and if x is the natural embedding of X into X ** , then by ...

Page 512

6 If Y is reflexive , then the closed unit

operator topology . Conversely , if the closed unit

in the weak operator topology , Y is reflexive . Define the BWO topology for B ( X ...

6 If Y is reflexive , then the closed unit

**sphere**of B ( X , Y ) is compact in the weakoperator topology . Conversely , if the closed unit

**sphere**of B ( X , Y ) is compactin the weak operator topology , Y is reflexive . Define the BWO topology for B ( X ...

Page 718

8 Let h be a harmonic function defined in the

space . Let 1 < p < 00,0 < K < . Suppose that for each r , 0 < r < 1 , the integral of

the function h ( rx ) | Pover the surface of the unit

8 Let h be a harmonic function defined in the

**sphere**Li - 12 ; < i in Euclidean n -space . Let 1 < p < 00,0 < K < . Suppose that for each r , 0 < r < 1 , the integral of

the function h ( rx ) | Pover the surface of the unit

**sphere**is SK . Putting h * ( x ) ...### What people are saying - Write a review

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### Contents

Preliminary Concepts | 1 |

B Topological Preliminaries | 10 |

Algebraic Preliminaries | 34 |

Copyright | |

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### 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

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