## Linear Operators: Spectral operators |

### From inside the book

Results 1-3 of 91

Page 2197

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

space X and let { Ea } be a monotone generalized

Ea } is ...

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

space X and let { Ea } be a monotone generalized

**sequence**( a monotone**sequence**) in B . Then , if { Ex } is increasing , lim Eqx = ( V Ec ) , « ex , while if {Ea } is ...

Page 2218

Let { Ex } be a weakly convergent generalized

its limit E is a projection . It must be shown that { Ea } 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 { Ea } 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 { { n } consisting of eigenvectors of T .

We let Tun = dn Xn , and suppose that none of the eigenvalues dn is multiple (

that is , that the

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

We let Tun = dn Xn , and suppose that none of the eigenvalues dn is multiple (

that is , that the

**sequence**{ n } contains no repetitions ) and that do 70 for n 2 1 .### What people are saying - Write a review

We haven't found any reviews in the usual places.

### Contents

SPECTRAL OPERATORS | 1924 |

An Operational Calculus for Bounded Spectral | 1941 |

Part | 1950 |

Copyright | |

9 other sections not shown

### Other editions - View all

### Common terms and phrases

adjoint operator analytic apply arbitrary assume B-space Banach space Boolean algebra Borel sets boundary conditions bounded bounded operator Chapter clear closed commuting compact complex consider constant contained continuous converges Corollary corresponding countably additive defined Definition denote dense determined differential operator discrete domain elements equation equivalent established example exists extension fact finite follows formal formula given gives Hence Hilbert space hypothesis identity inequality integral invariant inverse Lemma limit linear linear operator Math Moreover multiplicity norm positive preceding present problem projections PROOF properties proved range regular resolution resolvent respectively restriction Russian satisfies scalar type seen sequence shown shows similar spectral measure spectral operator spectrum subset subspace sufficiently Suppose Theorem theory topology unbounded uniform uniformly unique valued vector weakly zero