Linear Operators, Part 2Interscience Publishers, 1963 - Algebra, Universal |
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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 869
... commutative B - algebra into the complex number system is continuous . 4 LEMMA . Let M be the set of maximal ideals in the commutative B - algebra X. Then x ( M ) = o ( x ) and sup ( M ) = lim a " / " . MЄM n PROOF . Since the element ...
... commutative B - algebra into the complex number system is continuous . 4 LEMMA . Let M be the set of maximal ideals in the commutative B - algebra X. Then x ( M ) = o ( x ) and sup ( M ) = lim a " / " . MЄM n PROOF . Since the element ...
Page 882
... commutative Banach algebra . 14 If ƒ is in L1 ( —∞ , ∞ ) , and if λ ( E ) = SÅ f ( s ) ds show that ( 2 * μ ) ( E ) ... ( commutative ) B - algebra has only trivial ideals , then it is isometrically isomorphic to the complex numbers . Show ...
... commutative Banach algebra . 14 If ƒ is in L1 ( —∞ , ∞ ) , and if λ ( E ) = SÅ f ( s ) ds show that ( 2 * μ ) ( E ) ... ( commutative ) B - algebra has only trivial ideals , then it is isometrically isomorphic to the complex numbers . Show ...
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