## Linear Operators: General theory |

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Page 519

Show that the operator T , when regarded as acting in L. ( S , E , u ) , is weakly

compact and that its

L be the space of Lebesgue

general ...

Show that the operator T , when regarded as acting in L. ( S , E , u ) , is weakly

compact and that its

**square**is compact . 58 Let ( S , E , u ) be a positive ... 60 LetL be the space of Lebesgue

**integrable**functions on [ 0 , 1 ] . Represent thegeneral ...

Page 781

4. On regular perturbations of an operator with a quasi. Circ . Mat . Palermo 38 ,

113–166 ( 1914 ) . Lidskis , V. B. 1. On the number of solutions with

.

4. On regular perturbations of an operator with a quasi. Circ . Mat . Palermo 38 ,

113–166 ( 1914 ) . Lidskis , V. B. 1. On the number of solutions with

**integrable****square**of the system of differential equations . -Y " ' + P ( t ) y = 2y . Doklady Akad.

Page 804

equations for operators belonging to the trace class of a general Banach space .

Proc . London Math . ... 45 , 674 ( 1949 ) .

**integral**equations . Bull . Amer . Math . Soc . ... On the Fredholm theory of**integral**equations for operators belonging to the trace class of a general Banach space .

Proc . London Math . ... 45 , 674 ( 1949 ) .

**integrable square**. J. London Math .### What people are saying - Write a review

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### Contents

B Topological Preliminaries | 10 |

quences | 26 |

Algebraic Preliminaries | 34 |

Copyright | |

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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