Linear Operators: Spectral theory |
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Page 915
... denote the restriction of T to the orthogonal complement ( z1 ) of H ( z1 ) . Since T and T * map H ( ≈1 ) into itself , T and T map t ( ) into itself . Thus it follows immediately that T2 is normal . = 2 2 Now select z , in ( z1 ) in ...
... denote the restriction of T to the orthogonal complement ( z1 ) of H ( z1 ) . Since T and T * map H ( ≈1 ) into itself , T and T map t ( ) into itself . Thus it follows immediately that T2 is normal . = 2 2 Now select z , in ( z1 ) in ...
Page 1126
... denote by the letter U 。. 0 λ Let S be a bounded operator in L2 ( C ) which commutes with each projection UZ1EU 。. Let 1 denote the function in L2 ( C ) which is identically equal to 1. If U1SU ( 1 ) = h ( x ) , then it is evident ...
... denote by the letter U 。. 0 λ Let S be a bounded operator in L2 ( C ) which commutes with each projection UZ1EU 。. Let 1 denote the function in L2 ( C ) which is identically equal to 1. If U1SU ( 1 ) = h ( x ) , then it is evident ...
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
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