Linear Operators: Spectral theory |
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Page 873
... Hausdorff space then it is homeomorphic with the structure space of C ( 4 ) . 18 COROLLARY . If Д , and Д are compact Hausdorff spaces such that the algebras С ( Д1 ) and C ( IX.2.17 873 COMMUTATIVE B - ALGEBRAS.
... Hausdorff space then it is homeomorphic with the structure space of C ( 4 ) . 18 COROLLARY . If Д , and Д are compact Hausdorff spaces such that the algebras С ( Д1 ) 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 x - 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 x - measure , III.9.47 ( 174 ) Hausdorff space , criterion for ...
Contents
SPECTRAL THEORY Self Adjoint Operators in Hilbert Space | 858 |
BAlgebras | 859 |
Commutative BAlgebras | 868 |
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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 deficiency indices Definition denote dense eigenvalues element equation essential spectrum Exercise exists finite dimensional follows from Lemma follows from Theorem follows immediately formal differential operator formally self adjoint formula Fourier function defined function f Hence Hilbert space Hilbert-Schmidt operator identity inequality integral interval isometric isomorphism kernel L₁ L₁(R L₂ L₂(I L₂(R Lemma Let f linear linearly independent mapping matrix measure neighborhood non-zero norm open set operators in Hilbert orthogonal orthonormal basis Plancherel's theorem positive preceding lemma PROOF prove real axis real numbers satisfies sequence solution spectral spectral theorem square-integrable subspace Suppose T₁ T₂ theory To(t topology tr(T unique unitary vanishes vector zero