Linear Operators, Part 2 |
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Page 1900
... properties , III.14 space of , definition , IV.2.24 ( 242 ) properties , IV.15 Annihilator of a set , II.4.17 ( 72 ) Arens ' lemma , IX.3.5 ( 875–876 ) Arzelà theorem , on continuity of limit function , IV.6.11 ( 268 ) remarks ...
... properties , III.14 space of , definition , IV.2.24 ( 242 ) properties , IV.15 Annihilator of a set , II.4.17 ( 72 ) Arens ' lemma , IX.3.5 ( 875–876 ) Arzelà theorem , on continuity of limit function , IV.6.11 ( 268 ) remarks ...
Page 1901
... properties , VI.9.9 ( 512 ) Bounded variation of a function , ad- ditional properties , IV.15 ( 378 ) criterion to be , IV.13.73 ( 350 ) definition , III.5.15 ( 140 ) generating Borel - Stieltjes measure , ( 142 ) integral with respect ...
... properties , VI.9.9 ( 512 ) Bounded variation of a function , ad- ditional properties , IV.15 ( 378 ) criterion to be , IV.13.73 ( 350 ) definition , III.5.15 ( 140 ) generating Borel - Stieltjes measure , ( 142 ) integral with respect ...
Page 1902
... properties , I.4.4–5 ( 10 ) Closed sphere , II.4.1 ( 70 ) Closed unit sphere , II.3.1 ( 59 ) Closure of a set , criterion to be in , 1.7.2 ( 27 ) definition , I.4.9 ( 11 ) properties of the closure operation , 1.4.10-11 ( 11-12 ) ...
... properties , I.4.4–5 ( 10 ) Closed sphere , II.4.1 ( 70 ) Closed unit sphere , II.3.1 ( 59 ) Closure of a set , criterion to be in , 1.7.2 ( 27 ) definition , I.4.9 ( 11 ) properties of the closure operation , 1.4.10-11 ( 11-12 ) ...
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 Haar measure Hence Hilbert space Hilbert-Schmidt operator identity inequality integral interval isometric isomorphism kernel L₁ L₁(R L₂(I L₂(R Lemma Let f linearly independent mapping matrix measure neighborhood non-zero norm operators in Hilbert orthogonal orthonormal basis Plancherel's theorem positive preceding lemma PROOF prove real axis real numbers satisfies sequence solution spectral spectral theorem square-integrable subspace Suppose T₁ T₂ theory To(t topology tr(T transform unique unitary vanishes vector zero