Linear Operators, Part 2Interscience Publishers, 1963 - Algebra, Universal |
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Page 879
... contains a normal operator T , its adjoint T * , and the identity I is a commutative B * -algebra . Thus we may state the following corollary . 15 COROLLARY . Let T be a normal operator in a Hilbert space H and let B * ( T ) be the ...
... contains a normal operator T , its adjoint T * , and the identity I is a commutative B * -algebra . Thus we may state the following corollary . 15 COROLLARY . Let T be a normal operator in a Hilbert space H and let B * ( T ) be the ...
Page 995
... containing the remainder of o ( f * q ) . It follows from Lemma 12 that the set ( h * f * p ) contains at most the single point m 。 and hence , from Theorem 16 and Lemma 3.1 ( d ) , that there is a number « with ( h * f * ∞ ) ( x ) ...
... containing the remainder of o ( f * q ) . It follows from Lemma 12 that the set ( h * f * p ) contains at most the single point m 。 and hence , from Theorem 16 and Lemma 3.1 ( d ) , that there is a number « with ( h * f * ∞ ) ( x ) ...
Page 996
... contains no interior point of o ( y ) . Hence o ( ƒ * q ) is a closed subset of the boundary of o ( 9 ) . Since f * q = 0 it follows from Lemma 11 ( a ) that o ( fp ) is not void . Thus , by hypothesis , o ( f ) contains an isolated ...
... contains no interior point of o ( y ) . Hence o ( ƒ * q ) is a closed subset of the boundary of o ( 9 ) . Since f * q = 0 it follows from Lemma 11 ( a ) that o ( fp ) is not void . Thus , by hypothesis , o ( f ) contains an isolated ...
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