Linear Operators, Part 2Interscience Publishers, 1963 - Algebra, Universal |
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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 ... HILBERT - SCHMIDT 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 ... HILBERT - SCHMIDT OPERATORS Hilbert-Schmidt Operators Unbounded Operators in Hilbert Space 1 Introduction.
Page 1010
... Hilbert- Schmidt operators may be defined as follows . DEFINITION . Let { x , xe 4 } be a complete orthonormal set in the Hilbert space H. A bounded linear operator T is said to be a Hilbert - Schmidt operator in case the quantity || T ...
... Hilbert- Schmidt operators may be defined as follows . DEFINITION . Let { x , xe 4 } be a complete orthonormal set in the Hilbert space H. A bounded linear operator T is said to be a Hilbert - Schmidt operator in case the quantity || T ...
Page 1132
... Hilbert - Schmidt operator K in L ( A ) satisfying the equality in ( iv ) . It is plain from Theorem 4 that the Hilbert space o of Theorem 4 is a subspace of L2 ( A ) . The orthogonal projection E of L2 ( A ) onto Ho is readily verified ...
... Hilbert - Schmidt operator K in L ( A ) satisfying the equality in ( iv ) . It is plain from Theorem 4 that the Hilbert space o of Theorem 4 is a subspace of L2 ( A ) . The orthogonal projection E of L2 ( A ) onto Ho is readily verified ...
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 Haar measure 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 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 transform unique unitary vanishes vector zero