Linear Operators: Spectral theory |
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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 ƒƒ ( 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 ƒƒ ( s ) v ( ds ) ...
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 KH 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 KH and a self adjoint projection valued additive ...
Page 958
... additive on Bo 0 To see that is countably additive on Bo let e „ , n ≥ 1 , be disjoint sets in Bo whose union e is also in Bo . Let rnen Uen + 1 ... , so that E ( r ) g0 for every g in L ( R ) and , by Lemma 5 , Y ( g , y ( e ...
... additive on Bo 0 To see that is countably additive on Bo let e „ , n ≥ 1 , be disjoint sets in Bo whose union e is also in Bo . Let rnen Uen + 1 ... , so that E ( r ) g0 for every g in L ( R ) and , by Lemma 5 , Y ( g , y ( e ...
Contents
BAlgebras | 859 |
Bounded Normal Operators in Hilbert Space | 887 |
Miscellaneous Applications | 937 |
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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 complex numbers converges Corollary deficiency indices Definition denote dense domain eigenfunctions 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 kernel L₁(R L₂(I L₂(R Lemma Let f linearly independent mapping Math matrix measure neighborhood norm open set operators in Hilbert orthogonal orthonormal partial differential operator Plancherel's theorem positive preceding lemma prove real axis real numbers representation satisfies Section sequence solution spectral spectral theory square-integrable subspace Suppose symmetric operator T₁ T₂ theory To(t topology unique unitary vanishes vector zero