Linear Operators, Part 2 |
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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 x M , the vectors Thx , 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 x M , the vectors Thx , n = 0 ...
Page 1218
... restriction of f to the complement of o is continuous . PROOF . If the restrictions fo , g | d are continuous then so is the restriction ( af + 8g ) on 8 and thus the class of measurable functions . having the required property is a ...
... restriction of f to the complement of o is continuous . PROOF . If the restrictions fo , g | d are continuous then so is the restriction ( af + 8g ) on 8 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 B1 ( x ) -0 , C , ( x ) = 0 , j = 1 ij i = 1 , . . , n , where ( 0¿ ; ) is any matrix satisfying Σ " = 10ijŌki = dik . Moreover , every such restriction ...
... restriction of T * to the subspace of D ( T * ) determined by the boundary conditions n B1 ( x ) -0 , C , ( x ) = 0 , j = 1 ij i = 1 , . . , n , where ( 0¿ ; ) is any matrix satisfying Σ " = 10ijŌki = dik . Moreover , every such restriction ...
Contents
BAlgebras | 861 |
Commutative BAlgebras | 868 |
Commutative BAlgebras | 874 |
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adjoint extension adjoint operator algebra analytic B-algebra B*-algebra Borel set boundary conditions boundary values bounded operator C₁ closed closure coefficients compact operator complex numbers constant 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 prove real axis real numbers satisfies sequence solution spectral spectral theorem square-integrable subset subspace Suppose T₁ T₂ theory To(t topology unique unitary vanishes vector zero