## Linear Operators, Part 2 |

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Page 871

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

over Y. Pnoor. By Lemma 4-, y(.I) = a(y) and thus the correspondence EH2 -> y(fl)

"t) ...

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

**homeomorphic**to a closed subset 0/ the Cartesian product Pa(y) where y variesover Y. Pnoor. By Lemma 4-, y(.I) = a(y) and thus the correspondence EH2 -> y(fl)

"t) ...

Page 973

Since the function h(a:) = em satisfies the identities ]h(w)] = 1 and h(.z'+y) = h(.r)h(

y), the map m -> t(m) maps R onto all of R. To see that the map t is a

z't(m))2}§ ...

Since the function h(a:) = em satisfies the identities ]h(w)] = 1 and h(.z'+y) = h(.r)h(

y), the map m -> t(m) maps R onto all of R. To see that the map t is a

**homeomorphism**note that |[~'¢» °l—l$, mll = |1—¢m('"'| = {(l—cos act(m))*-1-(sin .z't(m))2}§ ...

Page 981

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

.1 —> .11 is a

3.15 that the structure space of QI1 is

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

.1 —> .11 is a

**homeomorphism**. Q.E.D. It follows from Theorem 1 and Theorem3.15 that the structure space of QI1 is

**homeomorphic**to the compactification R u ...### What people are saying - Write a review

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### Contents

SPECTRAL THEORY | 858 |

Bounded Normal Operators in Hilbert Space | 887 |

Miscellaneous Applications | 937 |

Copyright | |

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Acad adjoint extension adjoint operator algebra Amer analytic B-algebra Banach spaces Borel set boundary conditions boundary values bounded operator closed closure coefficients complex numbers continuous function converges Corollary deficiency indices Definition denote dense differential equations Doklady Akad domain eigenfunctions eigenvalues element essential spectrum exists finite dimensional follows from Lemma follows from Theorem follows immediately formal differential operator formally self adjoint formula Fourier function f Haar measure Hence Hilbert space Hilbert-Schmidt operator hypothesis identity inequality integral interval kernel Lemma Let f linear operator linearly independent mapping matrix measure Nauk SSSR N. S. neighborhood norm open set operators in Hilbert orthogonal orthonormal Paoor partial differential operator Pnoor positive preceding lemma Proc prove real axis real numbers representation satisfies second order Section sequence singular solution spectral set spectral theory square-integrable subspace Suppose symmetric operator topology transform unique unitary vanishes vector zero