Linear Operators: Spectral theory |
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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 / 3 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 which contains properly determines an ideal in X / defined as ...
... ideal is two - sided and the quotient algebra X / 3 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 which contains properly determines an ideal in X / defined as ...
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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A₁ 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 countably deficiency indices Definition denote dense eigenfunctions eigenvalues element equation essential spectrum Exercise exists f₁ finite dimensional follows from Lemma follows from Theorem formal differential operator formally self adjoint formula Fourier function f Haar measure Hence Hilbert space Hilbert-Schmidt operator homomorphism identity inequality infinity integral interval kernel L₁ L₁(R L₂ L₂(I L₂(R Lemma Let f linearly independent mapping matrix measure neighborhood non-zero norm operators in Hilbert orthogonal Plancherel's theorem positive preceding lemma prove real axis real numbers satisfies sequence shows solution spectral set spectral theorem square-integrable subset subspace Suppose T₁ T₂ theory To(t topology tr(T transform uniformly unique unitary vanishes vector zero