## Linear Operators: General theory |

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Page 458

16 for notation ) which take on only the

every

point if and only if ( x + y + \ + y unless x and y are linearly dependent . A space ...

16 for notation ) which take on only the

**values**0 and 1 . Show that ... 7 Show thatevery

**boundary**point of the closed unit sphere S of a B - space X is an extremalpoint if and only if ( x + y + \ + y unless x and y are linearly dependent . A space ...

Page 737

Integration of functions with values in a Banach space . Trans . Amer . Math . Soc

. 38 , 357 – 378 ( 1935 ) . 5 . ... Trans . Amer . Math . Soc . 9 , 219 - 231 ( 1908 ) . 3

.

Integration of functions with values in a Banach space . Trans . Amer . Math . Soc

. 38 , 357 – 378 ( 1935 ) . 5 . ... Trans . Amer . Math . Soc . 9 , 219 - 231 ( 1908 ) . 3

.

**Boundary value**and expansion problems of ordinary linear REFERENCES 737.Page 763

The least cluster point of the spectrum of

Math . 70 , 847 - 855 ( 1948 ) . 2 . The gaps in the essential spectra of wave

equations . Amer . J . Math . 72 , 849 - 862 ( 1950 ) . Hartman , P . , and Wintner ,

A . 1 .

The least cluster point of the spectrum of

**boundary value**problems . Amer . J .Math . 70 , 847 - 855 ( 1948 ) . 2 . The gaps in the essential spectra of wave

equations . Amer . J . Math . 72 , 849 - 862 ( 1950 ) . Hartman , P . , and Wintner ,

A . 1 .

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### Contents

B Topological Preliminaries | 10 |

quences | 26 |

Algebraic Preliminaries | 34 |

Copyright | |

80 other sections not shown

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### Common terms and phrases

Acad algebra Amer analytic applied arbitrary assumed B-space Banach Banach spaces bounded called clear closed compact complex condition contains continuous functions converges convex Corollary countably additive defined DEFINITION denote dense determined differential disjoint Doklady Akad 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 operator positive measure problem Proc PROOF properties proved respect Russian satisfies scalar seen semi-group separable sequence set function Show shown sphere statement subset sufficient Suppose Theorem theory topological space topology transformations u-measurable uniform uniformly unique unit valued vector weak weakly compact zero