## Linear Operators: General theory |

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Page 72

( c ) If X is a reflective B - space and 3 is a closed

( c ) If X is a reflective B - space and 3 is a closed

**subspace**of X , show that 311 = 3. Is the result true if X is not reflexive ? 19 If X is a reflexive B - space , and 3 is a closed**subspace**of X , show , using Exercise 18 ...Page 420

On the other hand , if X is a

On the other hand , if X is a

**subspace**of yt , then each element ye y determines the linear functional f , on X defined by 1 , ( x ) = x ( y ) , X e X , and the**subspace**I { , \ y e Y } CX * is obviously total .Page 504

Then there exists a closed separable

Then there exists a closed separable

**subspace**y of X such that M is equivalent to a**subspace**of Y * . Proof . Let { 2 * } be a countable dense subset of M , and let { xmn } , m , n = 1 , 2 , ... , belong to X and satisfy the relations ...### 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