Linear Operators, Part 2Interscience Publishers, 1963 - Algebra, Universal |
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Page 958
... disjoint . Thus y ( e , ) and ( e ) are orthogonal whenever e , and e , are disjoint . Hence if e , and e are disjoint then ¥ ( e1 ○ e2 ) = E ( e1 ~ е2 ) ¥ ( е1 ~ е2 ) = = [ E ( e ) + E ( e2 ) ] y ( e1 ~ € 2 ) E ( e ) y ( e1 e2 ) + E ...
... disjoint . Thus y ( e , ) and ( e ) are orthogonal whenever e , and e , are disjoint . Hence if e , and e are disjoint then ¥ ( e1 ○ e2 ) = E ( e1 ~ е2 ) ¥ ( е1 ~ е2 ) = = [ E ( e ) + E ( e2 ) ] y ( e1 ~ € 2 ) E ( e ) y ( e1 e2 ) + E ...
Page 959
... disjoint sequence in B. It is clear that μ ( Uan ) ≥μ ( an ) , so that , if μ ( a ) = ∞ for any n , the equation μ ( Ua1 ) = Σμ ( an ) is trivially true . Hence we may and shall assume that ( an ) < ∞ for each n . Consequently ...
... disjoint sequence in B. It is clear that μ ( Uan ) ≥μ ( an ) , so that , if μ ( a ) = ∞ for any n , the equation μ ( Ua1 ) = Σμ ( an ) is trivially true . Hence we may and shall assume that ( an ) < ∞ for each n . Consequently ...
Page 1151
... disjoint closed subsets of R and if n is an integer , then there is an open set UCR such that AKCU and Ū ○ B = 6. This is true since for each pe A Kn there is an open set U ( p ) such that pЄ U ( p ) and U ( p ) ^ B = 4 ; by the ...
... disjoint closed subsets of R and if n is an integer , then there is an open set UCR such that AKCU and Ū ○ B = 6. This is true since for each pe A Kn there is an open set U ( p ) such that pЄ U ( p ) and U ( p ) ^ B = 4 ; by the ...
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