Linear Operators, Part 2 |
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Page 866
... ideal is also a right , left , or two - sided ideal . This shows that a maximal ideal is closed . Let 3 be a right ideal and order by inclusion the family of all right ideals which contain 3. An application of Zorn's lemma shows that ...
... ideal is also a right , left , or two - sided ideal . This shows that a maximal ideal is closed . Let 3 be a right ideal and order by inclusion the family of all right ideals which contain 3. An application of Zorn's lemma shows that ...
Page 868
... ideal is two - sided and the quotient algebra X / I is again a commutative algebra . It will be a B - algebra if is closed ( 1.13 ) . It is readily seen that every ideal J in X which contains properly determines an ideal ♬ in X / ỡ ...
... ideal is two - sided and the quotient algebra X / I is again a commutative algebra . It will be a B - algebra if is closed ( 1.13 ) . It is readily seen that every ideal J in X which contains properly determines an ideal ♬ in X / ỡ ...
Page 1162
... ideal is contained in a maximal ideal , but if an identity is not present this is not true and it becomes an important problem to find when a closed ideal is contained in a regular maximal ideal . Theorem 4.8 settles this question for ...
... ideal is contained in a maximal ideal , but if an identity is not present this is not true and it becomes an important problem to find when a closed ideal is contained in a regular maximal ideal . Theorem 4.8 settles this question for ...
Contents
BAlgebras | 859 |
Commutative BAlgebras | 868 |
Commutative BAlgebras | 874 |
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Common terms and phrases
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 domain 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 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 open set operators in Hilbert orthogonal orthonormal basis Plancherel's theorem positive preceding lemma 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