Linear Operators, Part 2Interscience Publishers, 1963 - Algebra, Universal |
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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 ( AB ) X = ( 4X ) ~ ( BX ) , and ( Av B ) X = ( 4X ) + ( 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 ( AB ) X = ( 4X ) ~ ( BX ) , and ( Av B ) X = ( 4X ) + ( 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 ∞ 9 ( E ) = Σ | Ex2 n = 1 ( 1+ | xn | 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 ∞ 9 ( E ) = Σ | Ex2 n = 1 ( 1+ | xn | 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 ( x ) . Thus , by ...
... 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 ( x ) . Thus , by ...
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