## Linear Operators: Spectral operators |

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Page 2197

Let B be a complete ( o - complete ) Boolean algebra of projections in the B -

space X and let { Ec } be a monotone generalized

Eq } is ...

Let B be a complete ( o - complete ) Boolean algebra of projections in the B -

space X and let { Ec } be a monotone generalized

**sequence**( a monotone**sequence**) in B . Then , if { Ea } is increasing , lim Eqz = ( V Eao , xe Ý , while if {Eq } is ...

Page 2218

Let { Ex } be a weakly convergent generalized

its limit E is a projection . It must be shown that { Ex } converges strongly to E . By

Lemma 6 , E is in B and so a consideration of the

...

Let { Ex } be a weakly convergent generalized

**sequence**in B and suppose thatits limit E is a projection . It must be shown that { Ex } converges strongly to E . By

Lemma 6 , E is in B and so a consideration of the

**sequence**{ Ea – E } shows that...

Page 2450

4 there exists a complete orthonormal basis { Xn } consisting of eigenvectors of T

. We let T ' xn = dn Xn , and suppose that none of the eigenvalues in is multiple (

that is , that the

4 there exists a complete orthonormal basis { Xn } consisting of eigenvectors of T

. We let T ' xn = dn Xn , and suppose that none of the eigenvalues in is multiple (

that is , that the

**sequence**{ an } contains no repetitions ) and that in # 0 for n 2 1 .### What people are saying - Write a review

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### Contents

SPECTRAL OPERATORS | 1924 |

Spectral Operators | 1925 |

Terminology and Preliminary Notions | 1928 |

Copyright | |

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