Linear Operators, Part 2Interscience Publishers, 1963 - Algebra, Universal |
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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 868
... algebra every ideal is two - sided and the quotient algebra X / is again a commutative algebra . It will be a B - algebra if 3 is closed ( 1.13 ) . It is readily seen that every ideal J in X which contains properly determines an ideal ...
... algebra every ideal is two - sided and the quotient algebra X / is again a commutative algebra . It will be a B - algebra if 3 is closed ( 1.13 ) . It is readily seen that every ideal J in X which contains properly determines an ideal ...
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 |
Commutative BAlgebras | 868 |
Commutative BAlgebras | 874 |
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Acad adjoint extension adjoint operator algebra Amer analytic B-algebra B*-algebra Banach Banach spaces Borel set boundary conditions boundary values bounded operator C₁ closed closure Co(I coefficients complex numbers continuous function converges Corollary deficiency indices Definition denote dense differential equations Doklady Akad domain eigenfunctions eigenvalues element essential spectrum exists follows from Lemma follows immediately formal differential operator formally self adjoint formula function f Haar measure Hence Hilbert space Hilbert-Schmidt operator identity inequality integral interval isometric isomorphism kernel L₁(R L₂(I L₂(R Lemma Let f linearly independent mapping Math matrix measure Nauk SSSR N. S. neighborhood norm open set operators in Hilbert orthogonal orthonormal positive Proc PROOF prove real axis satisfies sequence singular solution spectral spectral theory square-integrable subspace Suppose T₁ T₂ theory To(t topology transform unique unitary vanishes vector zero