Linear Operators: General theory |
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Page vi
The present work is written for the student as well as for the mature mathematician . Much of the text has grown directly out of lectures given by the authors over many years , and the two parts are designed to form suitable texts for a ...
The present work is written for the student as well as for the mature mathematician . Much of the text has grown directly out of lectures given by the authors over many years , and the two parts are designed to form suitable texts for a ...
Page 286
1 2 = p 9 = € j = E ХЕ discussion of the present section covers the space lo as well as the space L , ( S , E , u ) . THEOREM . If 1 < p < 0 and 1 / p + 1 / 9 = 1 , there is an isooo metric isomorphism between L * ( S , E , u ) and L ...
1 2 = p 9 = € j = E ХЕ discussion of the present section covers the space lo as well as the space L , ( S , E , u ) . THEOREM . If 1 < p < 0 and 1 / p + 1 / 9 = 1 , there is an isooo metric isomorphism between L * ( S , E , u ) and L ...
Page 660
In the present section conditions on an operator T in an arbitrary complex B - space X will be given which are necessary and sufficient for the conve of the averages 1 A ( n ) Σ Tm ce in X n - 1 n m = 0 of the iterates of T. These ...
In the present section conditions on an operator T in an arbitrary complex B - space X will be given which are necessary and sufficient for the conve of the averages 1 A ( n ) Σ Tm ce in X n - 1 n m = 0 of the iterates of T. These ...
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Contents
Preliminary Concepts | 1 |
B Topological Preliminaries | 10 |
quences | 26 |
Copyright | |
81 other sections not shown
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Common terms and phrases
Akad 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 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 separable sequence set function Show shown sphere statement subset sufficient Suppose Theorem theory topological space topology u-measurable uniform uniformly unique unit valued vector weak weakly compact zero