## Linear Operators, Part 1 |

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Page 251

It is clear that E is a

D is an orthogonal

O M , we ...

It is clear that E is a

**projection**, i.e. , E2 = E , and that E is an orthogonal**projection**. It is the uniquely determined orthogonal**projection**with EH = M. For ifD is an orthogonal

**projection**with DH = M then ED = D and , since ( I - D ) ÝCHO M , we ...

Page 481

Some useful elementary properties of

following lemmas . ... if and only if M , CM1 , or equivalently , if and only if Ni C Na

; ( b ) if E = E , + E2 - E , E ,, then E is a

– E ) X ...

Some useful elementary properties of

**projections**are summarized in thefollowing lemmas . ... if and only if M , CM1 , or equivalently , if and only if Ni C Na

; ( b ) if E = E , + E2 - E , E ,, then E is a

**projection**with EX = sp { M , UM , } and ( I– E ) X ...

Page 482

Thus , the family of all

... We conclude this section with a few remarks on

Let E be a

Thus , the family of all

**projections**in B ( X ) form a partially ordered set . Any two... We conclude this section with a few remarks on

**projections**in Hilbert space .Let E be a

**projection**in Hilbert space y , and let E * be its Hilbert space adjoint .### 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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### Other editions - View all

Linear Operators, Part 1 Nelson Dunford,Jacob T. Schwartz,William G. Bade,Robert G. Bartle Snippet view - 1958 |

### Common terms and phrases

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