## Linear Operators: General theory |

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Page 251

It is clear that E is a

D is an orthogonal

M ...

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 ) H CHOM ...

Page 480

Section 1 . 11 as a linear operator E for which E2 = E . If X is a linear topological

space , we shall require , from this point on , that E be continuous . 1 DEFINITION

.

**Projections**A**projection**in an arbitrary linear space X has been defined inSection 1 . 11 as a linear operator E for which E2 = E . If X is a linear topological

space , we shall require , from this point on , that E be continuous . 1 DEFINITION

.

Page 481

Some useful elementary properties of

following lemmas . ... CM , , or equivalently , if and only if Ni CNz ; ( b ) if E = E + E

, - E , E2 , then E is a

) if E ...

Some useful elementary properties of

**projections**are summarized in thefollowing lemmas . ... CM , , or equivalently , if and only if Ni CNz ; ( b ) if E = E + E

, - E , E2 , then E is a

**projection**with EX = sp { MUM , } and ( 1 - E ) X = Nin Nz ; ( c) if E ...

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### Contents

Metric Spaces | 19 |

Convergence and Uniform Convergence of Generalized | 26 |

Exercises | 33 |

Copyright | |

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