## Linear Operators: General theory |

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Page 481

Some useful elementary properties of

Some useful elementary properties of

**projections**are summarized in the following lemmas . ... E , if and only if M , CMı , or equivalently , if and only if N C Nz ; ( b ) if E = E + E , -E , E2 , then E is a**projection**with EX = sp { M ...Page 482

Thus , the family of all

Thus , the family of all

**projections**in B ( X ) form a partially ordered set . Any two commuting**projections**... Let E be a**projection**in Hilbert space H , and let E * be its Hilbert space adjoint . Then the identity ( Ex , ( I – E ) y ) ...Page 514

19 If E is a

19 If E is a

**projection**with n dimensional range , then E * is a**projection**with n dimensional range . 20 A**projection**has finite dimensional range if and only if it is compact . 21 A linear mapping E such that E2 = E is a**projection**...### What people are saying - Write a review

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### Contents

Preliminary Concepts | 1 |

The VitaliHahnSaks Theorem and Spaces of Measures | 7 |

B Topological Preliminaries | 10 |

Copyright | |

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Akad algebra Amer analytic applied arbitrary assumed B-space Banach Banach spaces bounded called clear closed closure complex condition Consequently contains continuous functions converges Corollary defined DEFINITION denote dense determined differential disjoint element equation equivalent everywhere Exercise exists extension field finite follows formula function f given Hence Hilbert space implies integral interval isomorphism Lebesgue Lemma limit linear functional linear operator linear space linear topological space Math means measure space metric space neighborhood norm open set operator problem Proc projection Proof properties proved range reflexive respect Russian 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