## Linear Operators: Spectral theory |

### From inside the book

Results 1-3 of 95

Page 888

where a, 6 are arbitrary

used the notations A A B and A v B for the intersection and union of two

commuting projections A and B. We recall that these operators are defined by the

...

where a, 6 are arbitrary

**spectral sets**and where q is the void set. Here we haveused the notations A A B and A v B for the intersection and union of two

commuting projections A and B. We recall that these operators are defined by the

...

Page 933

The

space, then von Neumann [3] defines a closed set S of the complex sphere to be

a

...

The

**spectral sets**of von Neumann. If T is a bounded linear operator in a Hilbertspace, then von Neumann [3] defines a closed set S of the complex sphere to be

a

**spectral set**of T if f(T) exists and |f(T) =< 1 whenever f is a rational function such...

Page 988

will introduce a basic notion in the study of the problem of spectral synthesis. 10

DEFINITION. The

the set of all characters on R which are contained in the Li-closed subspace St (p

) ...

will introduce a basic notion in the study of the problem of spectral synthesis. 10

DEFINITION. The

**spectral set**a (p) of a bounded measurable function p on R isthe set of all characters on R which are contained in the Li-closed subspace St (p

) ...

### What people are saying - Write a review

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

### Contents

BAlgebras | 859 |

Commutative BAlgebras | 868 |

Commutative BAlgebras | 874 |

Copyright | |

48 other sections not shown

### Other editions - View all

Linear Operators, Part 1 Nelson Dunford,Jacob T. Schwartz,William G. Bade,Robert G. Bartle Snippet view - 1958 |

### Common terms and phrases

additive adjoint adjoint operator algebra analytic assume B-algebra basis belongs Borel set boundary conditions boundary values bounded called clear closed closure coefficients commutative compact complex Consequently consider constant contains converges Corollary corresponding defined Definition denote dense determined domain eigenvalues element equal equation essential spectrum evident Exercise exists extension fact finite follows formal differential operator formula function function f given Hence Hilbert space ideal identity independent indices inequality integral interval isometric isomorphism Lemma linear mapping matrix measure multiplicity neighborhood norm normal operator obtained positive preceding present projection proof properties prove range regular representation respectively restriction result satisfies seen sequence shown singular solution spectral square-integrable statement subset subspace sufficiently Suppose symmetric Theorem theory topology transform unique unit vanishes vector zero