## Linear Operators: Spectral operators |

### From inside the book

Results 1-3 of 49

Page 2265

Now from Zorn's lemma we obtain a maximal family F of

each having uniform multiplicity . For each cardinal n let En be the supremum of

those FeF with m ( F ) = = n . If 0 #GS En , then G is the union of elements of B of ...

Now from Zorn's lemma we obtain a maximal family F of

**disjoint**elements of Beach having uniform multiplicity . For each cardinal n let En be the supremum of

those FeF with m ( F ) = = n . If 0 #GS En , then G is the union of elements of B of ...

Page 2266

A projection Ee B will be said to satisfy the countable chain condition if every

family of

denote by ( the set of all Ee B satisfying this condition . It will be shown that 6 is a

...

A projection Ee B will be said to satisfy the countable chain condition if every

family of

**disjoint**projections in B bounded by E is at most countable . We shalldenote by ( the set of all Ee B satisfying this condition . It will be shown that 6 is a

...

Page 2267

Since E el we may express E as the union of a sequence of

, each of which is the carrier of a vector x , with len $ 1 . Define xo = { n - 1 2- " xm

. Clearly Exo = xo . We assert E is the carrier of xo . For suppose that Fe B and ...

Since E el we may express E as the union of a sequence of

**disjoint**projections E, each of which is the carrier of a vector x , with len $ 1 . Define xo = { n - 1 2- " xm

. Clearly Exo = xo . We assert E is the carrier of xo . For suppose that Fe B and ...

### What people are saying - Write a review

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

### Contents

SPECTRAL OPERATORS 1937 1941 1945 XV Spectral Operators | 1924 |

Introduction | 1927 |

Terminology and Preliminary Notions | 1929 |

Copyright | |

32 other sections not shown

### Other editions - View all

### Common terms and phrases

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