## Linear Operators: Spectral theory |

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Page 868

If S is a closed ideal in the commutative B-algebra 3. then the quotient algebra 3/

8 is isometrically isomorphic to the field of

marimal. PRoof. If & is not maximal it is properly contained in an ideal and so 3/3

...

If S is a closed ideal in the commutative B-algebra 3. then the quotient algebra 3/

8 is isometrically isomorphic to the field of

**complex**numbers if and only if 3 ismarimal. PRoof. If & is not maximal it is properly contained in an ideal and so 3/3

...

Page 872

Nelson Dunford, Jacob T. Schwartz, William G. Bade, Robert G. Bartle.

variable that {P,(A)} also converges uniformly on G. For each A in G and each a in

3 define w(A) = lim P,(A) where {P,} is a sequence of polynomials with |P,(z)—w ...

Nelson Dunford, Jacob T. Schwartz, William G. Bade, Robert G. Bartle.

**complex**variable that {P,(A)} also converges uniformly on G. For each A in G and each a in

3 define w(A) = lim P,(A) where {P,} is a sequence of polynomials with |P,(z)—w ...

Page 887

There we associated with an operator T in a

of sets in the

defined as any subset of the spectrum or(T) which is both open and closed in the

...

There we associated with an operator T in a

**complex**B-space a Boolean algebraof sets in the

**complex**plane which were called spectral sets. A spectral set wasdefined as any subset of the spectrum or(T) which is both open and closed in the

...

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### Contents

SPECTRAL THEORY | 858 |

868 | 885 |

Miscellaneous Applications | 937 |

Copyright | |

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