Linear Operators: Spectral theory |
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Page 921
... perturbation in the strong operator topology and shall find it convenient to use the notation T →→ T to mean that T → T in the strong operator topology , i.e. , Tx → Tx for every x X.7 921 PERTURBATION THEORY Perturbation Theory.
... perturbation in the strong operator topology and shall find it convenient to use the notation T →→ T to mean that T → T in the strong operator topology , i.e. , Tx → Tx for every x X.7 921 PERTURBATION THEORY Perturbation Theory.
Page 929
... Perturbation theory . References for perturbation theory have already been given in Section VII.11 . The results in Section 7 are essentially due to Rellich [ 2 ; II ] . See also Riesz and Sz . - Nagy [ 1 ; Secs . 134-136 ] . Invariant ...
... Perturbation theory . References for perturbation theory have already been given in Section VII.11 . The results in Section 7 are essentially due to Rellich [ 2 ; II ] . See also Riesz and Sz . - Nagy [ 1 ; Secs . 134-136 ] . Invariant ...
Page 1916
... Perturbation of bounded linear opera- tors , remarks on , ( 611-612 ) study of , VII.6 , VII.8.1-2 ( 597–598 ) , VII.8.4-5 ( 598 ) Perturbation of infinitesimal genera- tor of a semi - group , ( 630–639 ) Peter - Weyl theorem , XI.1.4 ...
... Perturbation of bounded linear opera- tors , remarks on , ( 611-612 ) study of , VII.6 , VII.8.1-2 ( 597–598 ) , VII.8.4-5 ( 598 ) Perturbation of infinitesimal genera- tor of a semi - group , ( 630–639 ) Peter - Weyl theorem , XI.1.4 ...
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