Linear Operators, Part 2 |
From inside the book
Results 1-3 of 95
Page 1009
... Hilbert - Schmidt Operators ∞∞ , and In this section the theory of operators of the Hilbert - Schmidt type will be developed and ... HILBERT - SCHMIDT OPERATORS Hilbert-Schmidt Operators Unbounded Operators in Hilbert Space Introduction.
... Hilbert - Schmidt Operators ∞∞ , and In this section the theory of operators of the Hilbert - Schmidt type will be developed and ... HILBERT - SCHMIDT OPERATORS Hilbert-Schmidt Operators Unbounded Operators in Hilbert Space 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 H2H , and an orthogonal projection Q in 1 such that Ax = PQx , xes , P denoting the orthogonal projection of 1 on H. 29 Let { T } ... OPERATORS IN HILBERT SPACE XII.9.28.
... Hilbert space with 0 ≤ A≤I be given . Then there exists a Hilbert space H2H , and an orthogonal projection Q in 1 such that Ax = PQx , xes , P denoting the orthogonal projection of 1 on H. 29 Let { T } ... OPERATORS IN HILBERT SPACE XII.9.28.
Contents
BAlgebras | 859 |
Commutative BAlgebras | 868 |
Commutative BAlgebras | 874 |
Copyright | |
36 other sections not shown
Other editions - View all
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 domain 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 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 subspace Suppose T₁ T₂ theory To(t topology tr(T transform unique unitary vanishes vector zero