## Linear Operators: General theory |

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9. Exercises 1 The space B ( x , y ) is algebraically isomorphic to a subspace of the product Pxex Yz , where Ya = y , under the mapping T → PxxTx . Show that the strong topology of

9. Exercises 1 The space B ( x , y ) is algebraically isomorphic to a subspace of the product Pxex Yz , where Ya = y , under the mapping T → PxxTx . Show that the strong topology of

**operators**in B ( X , Y ) is identical with the usual ...Page 540

**operator**and the**operator**mapping into a weakly complete space X. Weakly compact**operators**from C [ 0 , 1 ] to X were treated by Sirvint ( 3 ] . A very incisive discussion of weakly compact**operators**with domain C ( S ) was given by ...Page 599

11 Let Xy be a closed subspace of a B - space X such that T X , CX for each

11 Let Xy be a closed subspace of a B - space X such that T X , CX for each

**operator**Tn in a sequence { Tn , n = 1 , 2 , ... } of commuting**operators**in B ( X ) . Let U , be the restriction of T , to X and let Vn : X / X1 + X / X ...### What people are saying - Write a review

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### Contents

Preliminary Concepts | 1 |

B Topological Preliminaries | 10 |

quences | 26 |

Copyright | |

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Akad algebra Amer analytic applied arbitrary assume B-space Banach Banach spaces bounded called clear closed compact complex Consequently contains converges convex Corollary countably additive defined DEFINITION denote dense determined differential disjoint domain 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 mean measure space metric space neighborhood norm o-field open set operator positive problem Proc PROOF properties proved range regular respect Russian satisfies scalar seen separable sequence set function Show shown sphere statement subset Suppose Theorem theory topological space topology transformations u-integrable u-measurable uniformly union unique unit valued vector weak zero