Linear Operators: Spectral theory |
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Page 881
... Banach algebra . Identify the maximal ideals . 8 Let K ( ) be the algebra of polynomials x = Στο αλλά with complex ... Banach algebra with a unique maximal ideal . 9 l1 The space of absolutely convergent series a = { a ,, — ∞ < n ...
... Banach algebra . Identify the maximal ideals . 8 Let K ( ) be the algebra of polynomials x = Στο αλλά with complex ... Banach algebra with a unique maximal ideal . 9 l1 The space of absolutely convergent series a = { a ,, — ∞ < n ...
Page 1856
... Banach algebras . Ann . of Math . ( 2 ) 51 , 615-628 ( 1950 ) . Representation of certain Banach algebras on Hilbert space . Duke Math . J. 18 , 27-39 ( 1951 ) . On spectral permanence for certain Banach algebras . Proc . Amer . Math ...
... Banach algebras . Ann . of Math . ( 2 ) 51 , 615-628 ( 1950 ) . Representation of certain Banach algebras on Hilbert space . Duke Math . J. 18 , 27-39 ( 1951 ) . On spectral permanence for certain Banach algebras . Proc . Amer . Math ...
Page 1900
... Banach limits , existence and proper- ties , II.4.22-23 ( 73 ) Banach - Stone theorem , on equivalence of C - spaces , V.8.8 ( 442 ) remarks on , ( 396–397 , 466 ) Banach theorem , on convergence of measurable functions , IV.11.2–3 ...
... Banach limits , existence and proper- ties , II.4.22-23 ( 73 ) Banach - Stone theorem , on equivalence of C - spaces , V.8.8 ( 442 ) remarks on , ( 396–397 , 466 ) Banach theorem , on convergence of measurable functions , IV.11.2–3 ...
Contents
BAlgebras | 859 |
Commutative BAlgebras | 868 |
Commutative BAlgebras | 874 |
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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 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 linear linearly independent mapping matrix measure neighborhood non-zero norm open set operators in Hilbert orthogonal orthonormal basis Plancherel's theorem positive preceding lemma PROOF prove real axis satisfies sequence solution spectral spectral theorem square-integrable subset subspace Suppose T₁ T₁(t T₂ theory To(t topology tr(T unique unitary vanishes vector zero