Linear Operators: Spectral theory |
From inside the book
Results 1-3 of 91
Page 860
... algebra L1 ( -∞ , ∞ ) with convolution as multiplication is a commutative algebra with an involution defined by f * ( s ) = f ( −s ) . It fails to be a B - algebra because it lacks a unit e . We shall show how a unit may be adjoined ...
... algebra L1 ( -∞ , ∞ ) with convolution as multiplication is a commutative algebra with an involution defined by f * ( s ) = f ( −s ) . It fails to be a B - algebra because it lacks a unit e . We shall show how a unit may be adjoined ...
Page 875
... algebra B ( § ) of all bounded linear operators in Hilbert space in which the operation of involution is defined by equation ( i ) is a B * -algebra . Our chief objective in this section is to characterize commutative B * -algebras . It ...
... algebra B ( § ) of all bounded linear operators in Hilbert space in which the operation of involution is defined by equation ( i ) is a B * -algebra . Our chief objective in this section is to characterize commutative B * -algebras . It ...
Page 979
... algebra A of the preceding section , we have met before . For convenience , its definition and some of its ... algebra under convolution as multiplication and the mapping f → T ( f ) is a con- tinuous isomorphism of the algebra L1 ( R ) ...
... algebra A of the preceding section , we have met before . For convenience , its definition and some of its ... algebra under convolution as multiplication and the mapping f → T ( f ) is a con- tinuous isomorphism of the algebra L1 ( R ) ...
Contents
BAlgebras | 859 |
Bounded Normal Operators in Hilbert Space | 887 |
Miscellaneous Applications | 937 |
Copyright | |
37 other sections not shown
Other editions - View all
Common terms and phrases
adjoint extension adjoint operator algebra analytic B-algebra B*-algebra Borel set boundary conditions boundary values bounded operator C₁ closed closure Co(I coefficients complex numbers converges Corollary deficiency indices Definition denote dense domain eigenfunctions eigenvalues element essential spectrum 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 kernel L₁(R L₂(I L₂(R Lemma Let f linearly independent mapping Math matrix measure neighborhood norm open set operators in Hilbert orthogonal orthonormal partial differential operator Plancherel's theorem positive preceding lemma prove real axis real numbers representation satisfies Section sequence solution spectral spectral theory square-integrable subspace Suppose symmetric operator T₁ T₂ theory To(t topology unique unitary vanishes vector zero