Linear Operators: Spectral theory |
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Page 1095
... uniform topology of operators , ( Corollary VI.5.5 ) , there exists a compact operator T such that T → T in the uniform topology . Thus , by Corollary 4 ( a ) , limm∞x ( Tn - Tm ) = μ ( T - T ) . It follows that N Σμ . ( Τη k = 1 ...
... uniform topology of operators , ( Corollary VI.5.5 ) , there exists a compact operator T such that T → T in the uniform topology . Thus , by Corollary 4 ( a ) , limm∞x ( Tn - Tm ) = μ ( T - T ) . It follows that N Σμ . ( Τη k = 1 ...
Page 1904
... uniform , criteria for , III.6.2-3 ( 145 ) , III.6.12 ( 149 ) definition , III.6.1 ( 145 ) uniform , definition 1.7.1 ( 26 ) properties , I.7.6-7 ( 28-29 ) Convergence of sequences , generaliz- ed , I.7.1-7 ( 26–29 ) in a metric space ...
... uniform , criteria for , III.6.2-3 ( 145 ) , III.6.12 ( 149 ) definition , III.6.1 ( 145 ) uniform , definition 1.7.1 ( 26 ) properties , I.7.6-7 ( 28-29 ) Convergence of sequences , generaliz- ed , I.7.1-7 ( 26–29 ) in a metric space ...
Page 1922
... Uniform boundedness principle , in B- spaces , II.3.20-21 ( 66 ) discussion of , ( 80-82 ) in F - spaces , II.1.11 ( 52 ) for measures , IV.9.8 ( 309 ) Uniform continuity , of an almost pe- riodic function , IV.7.4 ( 283 ) criterion for ...
... Uniform boundedness principle , in B- spaces , II.3.20-21 ( 66 ) discussion of , ( 80-82 ) in F - spaces , II.1.11 ( 52 ) for measures , IV.9.8 ( 309 ) Uniform continuity , of an almost pe- riodic function , IV.7.4 ( 283 ) criterion for ...
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