Linear Operators: Spectral theory |
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Page 893
... bounded L - measurable functions on S into the B * -algebra of bounded operators on Hilbert space . Returning now to the general integral Sf ( s ) E ( ds ) where E is merely a bounded additive operator valued set function , we observe ...
... bounded L - measurable functions on S into the B * -algebra of bounded operators on Hilbert space . Returning now to the general integral Sf ( s ) E ( ds ) where E is merely a bounded additive operator valued set function , we observe ...
Page 900
... bounded E - measurable scalar functions on S in such a way that each equivalence class consists of all E - measurable functions which differ from some bounded E - measurable function only on a set of E measure zero . That is , EB ( S ...
... bounded E - measurable scalar functions on S in such a way that each equivalence class consists of all E - measurable functions which differ from some bounded E - measurable function only on a set of E measure zero . That is , EB ( S ...
Page 1455
... bounded below , and whose essential spectrum σ ( 7 ) does not intersect the interval ( ∞ , 2 ) of the real axis ... bounded below , so that T is bounded below by Lemma 21. By Theorem 6.5 , σ ( T ) ~ ( − ∞ , λ — ε ) is void . Thus T is ...
... bounded below , and whose essential spectrum σ ( 7 ) does not intersect the interval ( ∞ , 2 ) of the real axis ... bounded below , so that T is bounded below by Lemma 21. By Theorem 6.5 , σ ( T ) ~ ( − ∞ , λ — ε ) is void . Thus T is ...
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