Linear Operators: Spectral theory |
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Page 1009
... Hilbert - Schmidt Operators In this section the theory of operators of the Hilbert - Schmidt type will be developed and rather deep and ... OPERATORS Hilbert-Schmidt Operators Unbounded Operators in Hilbert Space ✓ 1 Introduction.
... Hilbert - Schmidt Operators In this section the theory of operators of the Hilbert - Schmidt type will be developed and rather deep and ... OPERATORS Hilbert-Schmidt Operators Unbounded Operators in Hilbert Space ✓ 1 Introduction.
Page 1025
... Hilbert space . It is desired to generalize the notion of trace to certain operators in Hilbert space and at first glance it may appear that this notion is immediately available for Hilbert - Schmidt operators . However , this is not ...
... Hilbert space . It is desired to generalize the notion of trace to certain operators in Hilbert space and at first glance it may appear that this notion is immediately available for Hilbert - Schmidt operators . However , this is not ...
Page 1262
... Hilbert space with 0 ≤ A≤I be given . Then there exists a Hilbert space 1 2H , and an orthogonal projection Q in 1 such that Ax = PQx , x = H , P denoting the orthogonal projection of H1 on H ... OPERATORS IN HILBERT SPACE XII.9.28 XII .
... Hilbert space with 0 ≤ A≤I be given . Then there exists a Hilbert space 1 2H , and an orthogonal projection Q in 1 such that Ax = PQx , x = H , P denoting the orthogonal projection of H1 on H ... OPERATORS IN HILBERT SPACE XII.9.28 XII .
Contents
BAlgebras | 859 |
Commutative BAlgebras | 868 |
Commutative BAlgebras | 874 |
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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(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 satisfies sequence solution spectral spectral theorem square-integrable subset subspace Suppose T₁ T₁(t T₂ theory To(t topology tr(T unique unitary vanishes vector zero