## Linear Operators: Spectral theory |

### From inside the book

Results 1-3 of 49

Page 906

Unitary operators have a number of other characteristic properties. ... The relation

between unitary operators and complex numbers of unit modulus, Hermitian

operators and

Unitary operators have a number of other characteristic properties. ... The relation

between unitary operators and complex numbers of unit modulus, Hermitian

operators and

**real numbers**, and positive operators and positive numbers is ...Page 1744

... theorem be satisfied. Let x be any angular sector in the compler plane

including the positive real aris and the countable set of

(i) there eacists a

is in ...

... theorem be satisfied. Let x be any angular sector in the compler plane

including the positive real aris and the countable set of

**real numbers**a (V). Then,(i) there eacists a

**real number**K such that |R(Å; V)fter) s K|f|, fe L2(I), A # 2; (ii) if fis in ...

Page 1921

... I.8.1 (32) of

(49) topological space, definition, I.4.1 (10) study of, I.4–8 weak, in a B-space, (

419) weak* topology, (462) 3 and 3: “topologies in 3", (419) Total boundedness, ...

... I.8.1 (32) of

**real numbers**, (11) study of, I.4–8 topological group, definition, II.1.1(49) topological space, definition, I.4.1 (10) study of, I.4–8 weak, in a B-space, (

419) weak* topology, (462) 3 and 3: “topologies in 3", (419) Total boundedness, ...

### 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