Linear Operators, Part 2Interscience Publishers, 1963 - Algebra, Universal |
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Page 932
... additive ( resp . weakly countably additive ) function on to the set of positive operators on a Hilbert space § satis- fying F ( 6 ) = 0 and F ( S ) = I. Then there exists a Hilbert space 2 and a self adjoint projection valued additive ...
... additive ( resp . weakly countably additive ) function on to the set of positive operators on a Hilbert space § satis- fying F ( 6 ) = 0 and F ( S ) = I. Then there exists a Hilbert space 2 and a self adjoint projection valued additive ...
Page 958
... additive on Bo . 0 To see that μo is countably additive on Bo let e ,, n ≥1 , be disjoint sets in Bo whose union e is also in Bo . Let rn = en Uen + 1 ~ .. so that E ( r ) g0 for every g in L ( R ) and , by Lemma 5 , 0 ( g , y ( e ...
... additive on Bo . 0 To see that μo is countably additive on Bo let e ,, n ≥1 , be disjoint sets in Bo whose union e is also in Bo . Let rn = en Uen + 1 ~ .. so that E ( r ) g0 for every g in L ( R ) and , by Lemma 5 , 0 ( g , y ( e ...
Page 1803
... additive set functions and their application to generalization of a theorem of Lebesgue . Mat . Sbornik N. S. 20 ( 62 ) , 317-329 ( 1947 ) . ( Russian , English summary ) Math . Rev. 9 , 19 ( 1948 ) . On the basis of a family of ...
... additive set functions and their application to generalization of a theorem of Lebesgue . Mat . Sbornik N. S. 20 ( 62 ) , 317-329 ( 1947 ) . ( Russian , English summary ) Math . Rev. 9 , 19 ( 1948 ) . On the basis of a family of ...
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