Linear Operators, Part 2Interscience Publishers, 1963 - Algebra, Universal |
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Page 889
... set in the domain of a spectral measure satisfying ( iii ) is necessarily an ... Borel sets in the plane and which satisfies ( iv ) for every de B. This ... Borel sets ( v ) Σ E ( 8 , ) x i = 1 = ∞ E ( US ) x , x = H. i = 1 A spectral ...
... set in the domain of a spectral measure satisfying ( iii ) is necessarily an ... Borel sets in the plane and which satisfies ( iv ) for every de B. This ... Borel sets ( v ) Σ E ( 8 , ) x i = 1 = ∞ E ( US ) x , x = H. i = 1 A spectral ...
Page 894
... set functions whose values on a set oЄ _g ( 1 ) E ( dt ) . respectively . The integral Ss f ( s ) E ( ds are E ( od ) ... Borel set 8 in S and every pair æ , * with xe X , x * X * . It follows ( II.3.15 ) that E ( 8 ) = 0 . Thus if E and A ...
... set functions whose values on a set oЄ _g ( 1 ) E ( dt ) . respectively . The integral Ss f ( s ) E ( ds are E ( od ) ... Borel set 8 in S and every pair æ , * with xe X , x * X * . It follows ( II.3.15 ) that E ( 8 ) = 0 . Thus if E and A ...
Page 913
... Borel set e . Using the Lebesgue decomposition theorem ( III.4.14 ) , let { e } be a sequence of Borel sets such that Σv , ( e , ) = 0 , and such that if e is a Borel subset of the complement en of e , and Σ = v ( e ) 2-1 ( e ) = 0. Let ...
... Borel set e . Using the Lebesgue decomposition theorem ( III.4.14 ) , let { e } be a sequence of Borel sets such that Σv , ( e , ) = 0 , and such that if e is a Borel subset of the complement en of e , and Σ = v ( e ) 2-1 ( e ) = 0. Let ...
Contents
IX | 859 |
Bounded Normal Operators in Hilbert Space | 887 |
Miscellaneous Applications | 937 |
Copyright | |
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adjoint extension adjoint operator algebra analytic B-algebra B*-algebra Borel set boundary conditions boundary values bounded operator C₁ closed closure Co(I coefficients compact subset complex numbers continuous function converges Corollary deficiency indices Definition denote dense domain eigenvalues element essential spectrum 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(R L₂(I L₂(R Lemma Let f linear linearly independent mapping matrix measure neighborhood norm open set open subset orthonormal partial differential operator Plancherel's theorem positive PROOF prove real axis real numbers satisfies Section sequence solution spectral spectral theory square-integrable subspace Suppose T₁ T₁(t theory To(t topology unique unitary vanishes vector zero