## Linear Operators: General theory |

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Page 3

The restriction of a function f to a subset A of its

f | A . If | : A → B , and for each bef ( A ) there is only one a e A with f ( a ) = b , f is

said to have an inverse or to be one - to - one . The inverse function has

...

The restriction of a function f to a subset A of its

**domain**is sometimes denoted byf | A . If | : A → B , and for each bef ( A ) there is only one a e A with f ( a ) = b , f is

said to have an inverse or to be one - to - one . The inverse function has

**domain**f...

Page 230

Let f be an analytic function defined on a connected

plane and having its values in a complex B - space X . Then y ( x ) does not have

its maximum at any point of the

Let f be an analytic function defined on a connected

**domain**D in the complexplane and having its values in a complex B - space X . Then y ( x ) does not have

its maximum at any point of the

**domain**D , unless | ( ) is identically constant .Page 538

Nelson Dunford, Jacob T. Schwartz. G . Some miscellaneous convexity

inequalities . 48 ( Hadamard three circles theorem ) Let | be an analytic function

defined in the annular

Show that if ...

Nelson Dunford, Jacob T. Schwartz. G . Some miscellaneous convexity

inequalities . 48 ( Hadamard three circles theorem ) Let | be an analytic function

defined in the annular

**domain**a < ' z ' < b and having values in a B - space X .Show that if ...

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### Contents

B Topological Preliminaries | 10 |

Algebraic Preliminaries 84 | 34 |

Three Basic Principles of Linear Analysis | 49 |

Copyright | |

50 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

analytic applied arbitrary assumed B-space Borel bounded called Chapter clear closed complex condition Consequently constant contains continuous functions continuous linear converges Corollary countably additive defined DEFINITION denote dense determined dimensional disjoint element equation equivalent everywhere Exercise exists extended field finite follows formula function defined function f given Hence Hilbert identity implies inequality integral interval isometric isomorphism Lebesgue Lemma limit linear functional linear map linear operator linear space meaning metric space neighborhood norm obtained operator positive measure space projection PROOF properties proved range reflexive regular respect satisfies scalar seen separable sequence sequentially set function Show shown statement strongly subset subspace sufficient Suppose Theorem theory tion topology u-measurable uniform uniformly unique unit sphere valued vector weak weakly compact zero