Linear Operators: Spectral theory |
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Page 872
... topological space . 15 DEFINITION . A topological space A is completely regular if sets consisting of single points are closed and if for any point λ € △ and any closed set 4 , CA with 2 , 4 , there is a continuous function f defined ...
... topological space . 15 DEFINITION . A topological space A is completely regular if sets consisting of single points are closed and if for any point λ € △ and any closed set 4 , CA with 2 , 4 , there is a continuous function f defined ...
Page 1150
... topological space , a fact that was occasionally used in the text . Next we shall state the fundamental theorem concerning the existence of Haar measure and prove some of the more important elementary properties of this measure which ...
... topological space , a fact that was occasionally used in the text . Next we shall state the fundamental theorem concerning the existence of Haar measure and prove some of the more important elementary properties of this measure which ...
Page 1921
... space , definition , VII.7 ( 458 ) Strictly convex B - space , definition , VII.7 ( 458 ) Strong operator topology , definition , VI.1.2 ( 475 ) properties , VI.9.1–5 ( 511 ) , VI.9.11– 12 ( 512-513 ) Strong topology , in a normed space ...
... space , definition , VII.7 ( 458 ) Strictly convex B - space , definition , VII.7 ( 458 ) Strong operator topology , definition , VI.1.2 ( 475 ) properties , VI.9.1–5 ( 511 ) , VI.9.11– 12 ( 512-513 ) Strong topology , in a normed space ...
Contents
BAlgebras | 859 |
Commutative BAlgebras | 868 |
Commutative BAlgebras | 874 |
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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(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 satisfies sequence solution spectral spectral theorem square-integrable subset subspace Suppose T₁ T₁(t T₂ theory To(t topology tr(T unique unitary vanishes vector zero