Linear Operators: Spectral theory |
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Page 871
... homeomorphic to a closed subset of the Cartesian product Poly ) where y varies over Y. PROOF . By Lemma 4 , y ( M ) ... homeomorphism . Q.E.D. 12 COROLLARY . The structure space of a commutative B - algebra generated by a set Y has , as ...
... homeomorphic to a closed subset of the Cartesian product Poly ) where y varies over Y. PROOF . By Lemma 4 , y ( M ) ... homeomorphism . Q.E.D. 12 COROLLARY . The structure space of a commutative B - algebra generated by a set Y has , as ...
Page 873
... homeomorphism . The neighborhood ( z ) Ꭺ is mapped by 8-1 onto the set { Mx \ M2 = M ^ ‚ \ x¿ ( M2 ) −x¿ ( M ̧ ̧ ) ... homeomorphism . Q.E.D. 17 COROLLARY . If A is a compact Hausdorff space then it is homeomorphic with the structure ...
... homeomorphism . The neighborhood ( z ) Ꭺ is mapped by 8-1 onto the set { Mx \ M2 = M ^ ‚ \ x¿ ( M2 ) −x¿ ( M ̧ ̧ ) ... homeomorphism . Q.E.D. 17 COROLLARY . If A is a compact Hausdorff space then it is homeomorphic with the structure ...
Page 981
... homeomorphism . Q.E.D. 1 It follows from Theorem 1 and Theorem 3.15 that the structure space of A is homeomorphic to the compactification R { p } of the character group of R. The notation R { P } is justified since under the established ...
... homeomorphism . Q.E.D. 1 It follows from Theorem 1 and Theorem 3.15 that the structure space of A is homeomorphic to the compactification R { p } of the character group of R. The notation R { P } is justified since under the established ...
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