Linear Operators: Spectral theory |
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Page 888
... projections A and B. We recall that these operators are defined by the equations A B = AB , Av B = A + B - AB and that the intersection and union of two commuting projections are again projection operators . Also the ranges of the ...
... projections A and B. We recall that these operators are defined by the equations A B = AB , Av B = A + B - AB and that the intersection and union of two commuting projections are again projection operators . Also the ranges of the ...
Page 1123
... projections not contained in any larger set of subdiagonalizing projections . The family F contains the strong limit of any monotone - increasing and of any monotone - decreasing sequence of projections in F. ท ∞ PROOF . Our first ...
... projections not contained in any larger set of subdiagonalizing projections . The family F contains the strong limit of any monotone - increasing and of any monotone - decreasing sequence of projections in F. ท ∞ PROOF . Our first ...
Page 1124
... projections in F. We shall show below that there exists a Hermitian operator T such that all the projections E belong to the spectral resolution of T and such that each projection in the spectral resolution of T is the strong limit of ...
... projections in F. We shall show below that there exists a Hermitian operator T such that all the projections E belong to the spectral resolution of T and such that each projection in the spectral resolution of T is the strong limit of ...
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