## Linear Operators, Part 1 |

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Page 511

9 . Exercises 1 The space B ( X , Y ) is algebraically isomorphic to a subspace of

the product Poex Yz , where Yv = Y , under the mapping T → P8XTx . Show that

the strong topology of

9 . Exercises 1 The space B ( X , Y ) is algebraically isomorphic to a subspace of

the product Poex Yz , where Yv = Y , under the mapping T → P8XTx . Show that

the strong topology of

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

Nelson Dunford, Jacob T. Schwartz.

weakly complete space X . Weakly compact

treated by Sirvint [ 3 ] . A very incisive discussion of weakly compact

with ...

Nelson Dunford, Jacob T. Schwartz.

**operator**and the**operator**mapping into aweakly complete space X . Weakly compact

**operators**from C [ 0 , 1 ] to X weretreated by Sirvint [ 3 ] . A very incisive discussion of weakly compact

**operators**with ...

Page 599

( s ) ) for n = 1 , 2 , . . . , then in € L ( S , E , ) , and lim in exists . n + 00 11 Let X ; be

a closed subspace of a B - space X such that TnX , CX , for each

sequence { Tm , n = 1 , 2 , . . . } of commuting

( s ) ) for n = 1 , 2 , . . . , then in € L ( S , E , ) , and lim in exists . n + 00 11 Let X ; be

a closed subspace of a B - space X such that TnX , CX , for each

**operator**Tn in asequence { Tm , n = 1 , 2 , . . . } of commuting

**operators**in B ( X ) . Let Un be the ...### What people are saying - Write a review

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### Contents

Preliminary Concepts | 1 |

B Topological Preliminaries | 10 |

Algebraic Preliminaries | 34 |

Copyright | |

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### Common terms and phrases

algebra Amer analytic applied arbitrary assumed B-space Banach spaces bounded called clear closed compact operator complex condition Consequently constant contains continuous functions converges convex convex set Corollary countably additive defined DEFINITION denote dense determined differential dimensional disjoint domain element equation equivalent everywhere Exercise exists extension field finite follows formula function defined function f given Hence Hilbert space identity implies inequality integral interval Lebesgue Lemma limit linear functional linear operator linear space Math neighborhood norm obtained operator operator topology problem projection PROOF properties proved range reflexive representation respect satisfies scalar seen semi-group separable sequence set function Show shown statement subset subspace sufficient Suppose Theorem theory topology u-measurable uniform uniformly unique unit sphere valued vector weak weakly compact zero