Linear Operators: Spectral theory |
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Page 955
... denote the B * -algebra of operators Дo { al } , where I is the identity operator in the Hilbert space L2 ( R ) , and where Д , is the closure of A , in the uniform operator topology . The letter M will denote the space of maximal ...
... denote the B * -algebra of operators Дo { al } , where I is the identity operator in the Hilbert space L2 ( R ) , and where Д , is the closure of A , in the uniform operator topology . The letter M will denote the space of maximal ...
Page 1126
... denote by the letter U 。. = Let S be a bounded operator in L2 ( C ) which commutes with each projection U1EU . Let 1 denote the function in L2 ( C ) which is identically equal to 1. If USU 。( 1 ) h ( x ) , then it is evident that ...
... denote by the letter U 。. = Let S be a bounded operator in L2 ( C ) which commutes with each projection U1EU . Let 1 denote the function in L2 ( C ) which is identically equal to 1. If USU 。( 1 ) h ( x ) , then it is evident that ...
Page 1486
... denote the unit shift operator , so that ( Sf ) ( t ) = f ( t − 1 ) . Then , since the coefficients of 7 are ... denote n - dimensional unitary space . With each complex number 2 , associate a linear transformation B ( 2 ) in E " , as ...
... denote the unit shift operator , so that ( Sf ) ( t ) = f ( t − 1 ) . Then , since the coefficients of 7 are ... denote n - dimensional unitary space . With each complex number 2 , associate a linear transformation B ( 2 ) in E " , as ...
Contents
SPECTRAL THEORY Self Adjoint Operators in Hilbert Space | 858 |
BAlgebras | 859 |
Commutative BAlgebras | 868 |
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Common terms and phrases
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