Linear Operators, Part 2Interscience Publishers, 1963 - Algebra, Universal |
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Page 860
... algebra X is a mapping xx * of X into itself with the properties ( x + y ) * = x * + y * , ( xx ) * = αx * , ( xy ) * = y * x * ( x * ) * = x . All of the examples mentioned above , with the exception of L1 ( —∞ , ∞ ) and ... B - ALGEBRAS.
... algebra X is a mapping xx * of X into itself with the properties ( x + y ) * = x * + y * , ( xx ) * = αx * , ( xy ) * = y * x * ( x * ) * = x . All of the examples mentioned above , with the exception of L1 ( —∞ , ∞ ) and ... B - ALGEBRAS.
Page 868
Nelson Dunford, Jacob T. Schwartz. 2. Commutative B - Algebras In case is a commutative B - 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 ) ...
Nelson Dunford, Jacob T. Schwartz. 2. Commutative B - Algebras In case is a commutative B - 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 ) ...
Page 882
... algebra . 14 If ƒ is in L1 ( —∞ , ∞ ) , and if λ ( E ) = SÅ f ( s ) ds show that ( 2 * μ ) ( E ) = √ ̧ds [ ∞∞。 f ( s — t ) μ ( dt ) , E for every μ in the space M of Exercise 13. If μ ( E ) = SÅ g ( s ) ds for some g ... B - ALGEBRAS.
... algebra . 14 If ƒ is in L1 ( —∞ , ∞ ) , and if λ ( E ) = SÅ f ( s ) ds show that ( 2 * μ ) ( E ) = √ ̧ds [ ∞∞。 f ( s — t ) μ ( dt ) , E for every μ in the space M of Exercise 13. If μ ( E ) = SÅ g ( s ) ds for some g ... B - ALGEBRAS.
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