## Linear Operators: General theory |

### From inside the book

Results 1-3 of 80

Page 239

It consists of ordered n - tuples x = [ Q , ... , am ] of scalars Oj , ... , Olon and has

the

tuples ( Q2 , ... , obn ] of scalars Qy , . . . , Chen with the

It consists of ordered n - tuples x = [ Q , ... , am ] of scalars Oj , ... , Olon and has

the

**norm**n \ x1 = { 10 , \ " } l / p . The space 1 " is the linear space of all ordered n -tuples ( Q2 , ... , obn ] of scalars Qy , . . . , Chen with the

**norm**= sup loilo 1Sisn 4.Page 472

168 ] showed that the

and only if the function x , achieves its maximum at exactly one point . Mazur ( 1 ;

p . 78–79 ) proved that the same condition holds in B ( S ) , that the

168 ] showed that the

**norm**in C [ 0 , 1 ] is strongly differentiable at x , € C [ 0 , 1 ] ifand only if the function x , achieves its maximum at exactly one point . Mazur ( 1 ;

p . 78–79 ) proved that the same condition holds in B ( S ) , that the

**norm**in Lp ...Page 532

21 Show that the map T defined by 1 ( a ) ( Hardy ) ( T / ) ( a ) f ( y ) dy dy is a map

in Ly ( 0 , 0 ) of

y ) ( T / ) ( x ) Jo q + g is a map in L , ( 0,00 ) of

21 Show that the map T defined by 1 ( a ) ( Hardy ) ( T / ) ( a ) f ( y ) dy dy is a map

in Ly ( 0 , 0 ) of

**norm**p / ( p - 1 ) , p > 1 , ( b ) ( Hilbert , Schur , Hardy , M. Riesz ) f (y ) ( T / ) ( x ) Jo q + g is a map in L , ( 0,00 ) of

**norm**a ( sin ap ) -1 , p > 1 , ( c ) ...### What people are saying - Write a review

User Review - Flag as inappropriate

i want to read

### Contents

B Topological Preliminaries | 10 |

quences | 26 |

Algebraic Preliminaries | 34 |

Copyright | |

80 other sections not shown

### Other editions - View all

### 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