## Linear Operators: Spectral theory |

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Results 1-3 of 72

Page 860

It fails to be a B-algebra because it lacks a

be adjoined to such an algebra so that the extended algebra is a B-algebra. Let 3

: be an algebra satisfying all the requirements of a B-algebra except ...

It fails to be a B-algebra because it lacks a

**unit**e. We shall show how a**unit**maybe adjoined to such an algebra so that the extended algebra is a B-algebra. Let 3

: be an algebra satisfying all the requirements of a B-algebra except ...

Page 979

The algebra T(L1(R)) does not contain the

(L1(R)) in the uniform operator topology contain the

definition, the B-algebra obtained by adjoining the

...

The algebra T(L1(R)) does not contain the

**unit**I in B(L2(R)) nor does its closure T(L1(R)) in the uniform operator topology contain the

**unit**. The algebra QI is, bydefinition, the B-algebra obtained by adjoining the

**unit**I to T(L1(R)). Its elements...

Page 1493

If m + 1, then by the Weierstrass preparation theorem the inverse image of the

equal angles st/m at the point ào. If m > 1, not all of these arcs can possibly lie

along ...

If m + 1, then by the Weierstrass preparation theorem the inverse image of the

**unit**circle under the map opi includes a set of m analytic arcs all intersecting atequal angles st/m at the point ào. If m > 1, not all of these arcs can possibly lie

along ...

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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