## Linear Operators: Spectral theory |

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Page 871

The structure space of a commutative B-algebra generated by a set Y is

over Y. PRoof. By Lemma 4, y(~4) = o(s) and thus the correspondence Jo — y()')

defines ...

The structure space of a commutative B-algebra generated by a set Y is

**homeomorphic**to a closed subset of the Cartesian product Po (y) where y variesover Y. PRoof. By Lemma 4, y(~4) = o(s) and thus the correspondence Jo — y()')

defines ...

Page 973

Since |[a, m1]-sa, m]| = |sa, 0]–[a, m2–m1)|, the mapping to: R → R is a

tottom.), shows that t|mi-i-m2) = t|mi)+t(m2), and so t is an algebraic

Since |[a, m1]-sa, m]| = |sa, 0]–[a, m2–m1)|, the mapping to: R → R is a

**homeomorphism**. The identity eizt(m1+ma) - sa, m1 +m2] - [æ, m1] sa, m2] ex{tottom.), shows that t|mi-i-m2) = t|mi)+t(m2), and so t is an algebraic

**homeomorphism**.Page 981

Since these spaces are compact (IX.2.8) it follows from Lemma I.5.8 that the map.

4 – ~4.1 is a

3.15 that the structure space of Qs, is

p.} ...

Since these spaces are compact (IX.2.8) it follows from Lemma I.5.8 that the map.

4 – ~4.1 is a

**homeomorphism**. Q.E.D. It follows from Theorem 1 and Theorem3.15 that the structure space of Qs, is

**homeomorphic**to the compactification R U (p.} ...

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### Contents

SPECTRAL THEORY | 858 |

Bounded Normal Operators in Hilbert Space | 887 |

Miscellaneous Applications | 937 |

Copyright | |

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additive Akad algebra Amer analytic applied assume Banach spaces basis belongs Borel boundary conditions boundary values bounded called clear closed closure coefficients compact complete 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 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