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Page 873
... Hausdorff space then it is homeomorphic with the structure space of C ( A ) . 18 COROLLARY . If Д , and A2 are compact Hausdorff spaces such 2 that the algebras С ( Â1 ) and C IX.2.17 873 COMMUTATIVE B - ALGEBRAS.
... Hausdorff space then it is homeomorphic with the structure space of C ( A ) . 18 COROLLARY . If Д , and A2 are compact Hausdorff spaces such 2 that the algebras С ( Â1 ) and C IX.2.17 873 COMMUTATIVE B - ALGEBRAS.
Page 1832
... Hausdorff space . Doklady Akad . Nauk SSSR ( N. S. ) 27 , 427–430 ( 1940 ) . Sur l'espace des fonctions continues définies sur un bicompact de Hausdorff et ses sousespaces semiordonnés . Mat . Sbornik N. S. 13 ( 55 ) , 1–37 ( 1943 ) ...
... Hausdorff space . Doklady Akad . Nauk SSSR ( N. S. ) 27 , 427–430 ( 1940 ) . Sur l'espace des fonctions continues définies sur un bicompact de Hausdorff et ses sousespaces semiordonnés . Mat . Sbornik N. S. 13 ( 55 ) , 1–37 ( 1943 ) ...
Page 1909
... space of , V.3.1 ( 418 ) in weak and strong operator topolo- gies , VI.1.4 ( 477 ) Functions , of an element in a B ... Hausdorff maximality theorem , I.2.6 ( 6 ) Hausdorff α - measure , III.9.47 ( 174 ) Hausdorff space , criterion for ...
... space of , V.3.1 ( 418 ) in weak and strong operator topolo- gies , VI.1.4 ( 477 ) Functions , of an element in a B ... Hausdorff maximality theorem , I.2.6 ( 6 ) Hausdorff α - measure , III.9.47 ( 174 ) Hausdorff space , criterion for ...
Contents
BAlgebras | 859 |
Commutative BAlgebras | 868 |
Commutative BAlgebras | 874 |
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A₁ adjoint extension adjoint operator algebra analytic B-algebra Borel set boundary conditions boundary values bounded operator C₁ closed closure coefficients compact operator complex numbers continuous function converges Corollary countably deficiency indices Definition denote dense eigenfunctions eigenvalues element equation essential spectrum Exercise exists f₁ finite dimensional follows from Lemma follows from Theorem formal differential operator formally self adjoint formula Fourier function f Haar measure Hence Hilbert space Hilbert-Schmidt operator homomorphism identity inequality infinity integral interval kernel L₁ L₁(R L₂ L₂(I L₂(R Lemma Let f linearly independent mapping matrix measure neighborhood non-zero norm operators in Hilbert orthogonal Plancherel's theorem positive preceding lemma prove real axis real numbers satisfies sequence shows solution spectral set spectral theorem square-integrable subset subspace Suppose T₁ T₂ theory To(t topology tr(T transform uniformly unique unitary vanishes vector zero