## 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(~/) = g(y) and thus the correspondence SR → y(o)

defines a ...

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

**homeomorphic**to a closed subset of the Cartesian product Pa(y) where y variesover Y. Proof. By Lemma 4, y(~/) = g(y) and thus the correspondence SR → y(o)

defines a ...

Page 973

Since |sar, m1]—[æ, m]| - |[æ, 0]— [a, mg-mill, the mapping to: R → R is a

)} shows that tsmi--m2) = t|mi)+t(m2), and so t is an algebraic

To prove ...

Since |sar, m1]—[æ, m]| - |[æ, 0]— [a, mg-mill, the mapping to: R → R is a

**homeomorphism**. The identity e”***) = [a, m1 +m2] = [a, m1)[a, m2] - eiz(t(m)+t(ms)} shows that tsmi--m2) = t|mi)+t(m2), and so t is an algebraic

**homeomorphism**.To prove ...

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

BAlgebras | 859 |

Bounded Normal Operators in Hilbert Space | 887 |

Spectral Representation | 909 |

Copyright | |

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adjoint extension adjoint operator algebra Amer analytic B-algebra Banach Borel set boundary conditions boundary values bounded operator closed closure Cº(I coefficients complete 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 identity inequality integral interval kernel Lemma Let f linear operator linearly independent mapping Math matrix measure Nauk SSSR N.S. neighborhood norm open set operators in Hilbert orthogonal orthonormal Plancherel's theorem positive Proc PRoof prove real numbers satisfies sequence singular ſº solution spectral spectral set spectral theory square-integrable subspace Suppose theory To(r topology transform unique unitary vanishes vector zero