Linear Operators: Spectral theory |
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Page 931
... restriction of a normal operator to every invariant subspace is again normal . Wermer [ 5 ] studied the restriction of an operator T to a subspace M which is not invariant under T - 1 and such that for some aЄM , the vectors Tx , n = 0 ...
... restriction of a normal operator to every invariant subspace is again normal . Wermer [ 5 ] studied the restriction of an operator T to a subspace M which is not invariant under T - 1 and such that for some aЄM , the vectors Tx , n = 0 ...
Page 1218
... restriction of f to the complement of o is continuous . e PROOF . If the restrictions fo , g❘d are continuous then so is the restriction ( af + ßg ) | σ ~ d and thus the class of measurable functions having the required property is a ...
... restriction of f to the complement of o is continuous . e PROOF . If the restrictions fo , g❘d are continuous then so is the restriction ( af + ßg ) | σ ~ d and thus the class of measurable functions having the required property is a ...
Page 1239
... restriction of T * to the subspace of D ( T ) determined by the boundary conditions n B ( x ) — Σ0¿¡C , ( x ) = 0 , i = 1 , j = 1 ij j = 1 ij = .. , n , where ( 0 ,, ) is any matrix satisfying Σ - 100ki dik . Moreover , every such ...
... restriction of T * to the subspace of D ( T ) determined by the boundary conditions n B ( x ) — Σ0¿¡C , ( x ) = 0 , i = 1 , j = 1 ij j = 1 ij = .. , n , where ( 0 ,, ) is any matrix satisfying Σ - 100ki dik . Moreover , every such ...
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