## Linear Operators: Spectral theory |

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Page 865

Since the unit e in 3 is also in 30, it follows that a

in 3. Thus posa:) C p(r) or o(r) Coo(r). If Že bdy go(r), the boundary of oo(a), then

Ae—a is on the boundary of the group of

...

Since the unit e in 3 is also in 30, it follows that a

**regular**element in to is**regular**in 3. Thus posa:) C p(r) or o(r) Coo(r). If Že bdy go(r), the boundary of oo(a), then

Ae—a is on the boundary of the group of

**regular**elements of 30. Thus, by Lemma...

Page 1162

is isomorphic with the complex field, and it turns out that the

ideals of L1(R) are in one-to-one correspondence with the points of .40, i.e., with

all the maximal ideals of the algebra obtained by adjoining an identity to L1(R) ...

is isomorphic with the complex field, and it turns out that the

**regular**maximalideals of L1(R) are in one-to-one correspondence with the points of .40, i.e., with

all the maximal ideals of the algebra obtained by adjoining an identity to L1(R) ...

Page 1917

(See Reflexivity)

equation, XIII.6 ...

(See Reflexivity)

**Regular**closure, (462–463)**Regular**convexity, (462–463)**Regular**element in a B-algebra, IX.1.2 (861)**Regular**element in a ring, (40)**Regular**method of summability, II.4.35 (75)**Regular**point of a differentialequation, XIII.6 ...

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### 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