Linear Operators, Part 2Interscience Publishers, 1963 - Algebra, Universal |
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Page 893
... additive operator valued set function , we observe that the integral has been defined in terms of the uniform operator topology . It is clear that if v is a bounded additive vector valued set function on Σ , the integral Sf ( s ) v ( ds ) ...
... additive operator valued set function , we observe that the integral has been defined in terms of the uniform operator topology . It is clear that if v is a bounded additive vector valued set function on Σ , the integral Sf ( s ) v ( ds ) ...
Page 932
... additive ( resp . weakly countably additive ) function on to the set of positive operators on a Hilbert space H satis- fying F ( $ ) = 0 and F ( S ) = I. Then there exists a Hilbert space 25 and a self adjoint projection valued additive ...
... additive ( resp . weakly countably additive ) function on to the set of positive operators on a Hilbert space H satis- fying F ( $ ) = 0 and F ( S ) = I. Then there exists a Hilbert space 25 and a self adjoint projection valued additive ...
Page 958
... additive on B 。. 0 To see that μo is countably additive on B。 let e ,, n ≥ 1 , be disjoint sets in Bo whose union e is also in Bo . Let rn = en en + 10 so that E ( r ) g0 for every g in L2 ( R ) and , by Lemma 5 , ( g , y ( e ...
... additive on B 。. 0 To see that μo is countably additive on B。 let e ,, n ≥ 1 , be disjoint sets in Bo whose union e is also in Bo . Let rn = en en + 10 so that E ( r ) g0 for every g in L2 ( R ) and , by Lemma 5 , ( g , y ( e ...
Contents
BAlgebras | 859 |
Commutative BAlgebras | 868 |
Commutative BAlgebras | 874 |
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Acad adjoint extension adjoint operator algebra Amer analytic B-algebra B*-algebra Banach Banach spaces Borel set boundary conditions boundary values bounded operator C₁ closed closure Co(I coefficients complex numbers continuous function converges Corollary deficiency indices Definition denote dense differential equations Doklady Akad domain eigenfunctions eigenvalues element essential spectrum exists follows from Lemma follows immediately formal differential operator formally self adjoint formula 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 linearly independent mapping Math matrix measure Nauk SSSR N. S. neighborhood norm open set operators in Hilbert orthogonal orthonormal positive Proc PROOF prove real axis satisfies sequence singular solution spectral spectral theory square-integrable subspace Suppose T₁ T₂ theory To(t topology transform unique unitary vanishes vector zero