## Linear Operators, Part 1 |

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Page 481

Let E , and E , be commuting

, i = 1 , 2 , then ( a ) E , E , = 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

Let E , and E , be commuting

**projections**in a B - space X. = EzX , N ; = ( I – E ; ) X, i = 1 , 2 , then ( a ) E , E , = 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 , UM ...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 H , and let E * be its Hilbert space adjoint .Page 514

19 If E is a

dimensional range . 20 A

compact . 21 A linear mapping E such that E2 = E is a

bounded ) ...

19 If E is a

**projection**with n dimensional range , then E * is a**projection**with ndimensional range . 20 A

**projection**has finite dimensional range if and only if it iscompact . 21 A linear mapping E such that E2 = E is a

**projection**( i.e. , isbounded ) ...

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### Contents

Preliminary Concepts | 1 |

The VitaliHahnSaks Theorem and Spaces of Measures | 7 |

B Topological Preliminaries | 10 |

Copyright | |

87 other sections not shown

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