Linear Operators: Spectral theory |
From inside the book
Results 1-3 of 70
Page 888
... projections are again projection operators . Also the ranges of the intersection and union of two commuting projection operators are given by the equations ( A ^ B ) X = ( 4X ) ~ ( BX ) , and ( A v B ) X = ( AX ) + ( BX ) sp ( AX , BX ) ...
... projections are again projection operators . Also the ranges of the intersection and union of two commuting projection operators are given by the equations ( A ^ B ) X = ( 4X ) ~ ( BX ) , and ( A v B ) X = ( AX ) + ( BX ) sp ( AX , BX ) ...
Page 1123
... projections of a maximal totally ordered family of orthogonal projections commute . Let { x } be a dense set of vectors in Hilbert space and put ( E ) - ∞ Ex2 2 Σ n = 1 ( 1 + x , 2 ) 2 " Then ( E ) plainly increases with the projection ...
... projections of a maximal totally ordered family of orthogonal projections commute . Let { x } be a dense set of vectors in Hilbert space and put ( E ) - ∞ Ex2 2 Σ n = 1 ( 1 + x , 2 ) 2 " Then ( E ) plainly increases with the projection ...
Page 1126
... projection in the spectral resolution of T and hence each continuous function of T is a strong limit of linear combinations of the projections E ,, it follows from ( 1 ) that the closure in ( a ) of the vectors ( 4 ) is ( m ) . Thus ...
... projection in the spectral resolution of T and hence each continuous function of T is a strong limit of linear combinations of the projections E ,, it follows from ( 1 ) that the closure in ( a ) of the vectors ( 4 ) is ( m ) . Thus ...
Contents
BAlgebras | 859 |
Bounded Normal Operators in Hilbert Space | 887 |
Miscellaneous Applications | 937 |
Copyright | |
37 other sections not shown
Other editions - View all
Common terms and phrases
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