Linear Operators, Part 2 |
From inside the book
Results 1-3 of 85
Page 884
... results of this theory we present only a single result , due to von Neu- mann [ 2 ] , in this direction . If A is a collection of bounded linear opera- tors in a Hilbert space H , the centralizer ( 884 IX.5 IX . B - ALGEBRAS.
... results of this theory we present only a single result , due to von Neu- mann [ 2 ] , in this direction . If A is a collection of bounded linear opera- tors in a Hilbert space H , the centralizer ( 884 IX.5 IX . B - ALGEBRAS.
Page 1156
... result , which is dual to Theorem 8 . 0 9 THEOREM . If R is a discrete Abelian group , its character group R is compact . Ris The results of Sections 3 and 4 carry over for the case of discrete groups and many of them , for example ...
... result , which is dual to Theorem 8 . 0 9 THEOREM . If R is a discrete Abelian group , its character group R is compact . Ris The results of Sections 3 and 4 carry over for the case of discrete groups and many of them , for example ...
Page 1433
... result may be stated ; but here the basis for solutions of [ * ] may have a more complex form , involving logarithmic terms . We shall not give the details of this result here , but instead refer the reader to the excellent exposition ...
... result may be stated ; but here the basis for solutions of [ * ] may have a more complex form , involving logarithmic terms . We shall not give the details of this result here , but instead refer the reader to the excellent exposition ...
Contents
BAlgebras | 859 |
Commutative BAlgebras | 868 |
Commutative BAlgebras | 874 |
Copyright | |
36 other sections not shown
Other editions - View all
Common terms and phrases
adjoint extension adjoint operator algebra analytic B-algebra Borel set boundary conditions boundary values bounded operator C₁ closed closure coefficients compact operator complex numbers continuous function converges Corollary deficiency indices Definition denote dense domain eigenvalues element equation essential spectrum Exercise exists finite dimensional follows from Lemma follows from Theorem follows immediately formal differential operator formally self adjoint formula Fourier function defined function f Hence Hilbert space Hilbert-Schmidt operator identity inequality integral interval isometric isomorphism kernel L₁ L₁(R L₂(I L₂(R Lemma Let f linearly independent mapping matrix measure neighborhood non-zero norm open set operators in Hilbert orthogonal orthonormal basis Plancherel's theorem positive preceding lemma prove real axis real numbers satisfies sequence solution spectral spectral theorem square-integrable subspace Suppose T₁ T₂ theory To(t topology tr(T transform unique unitary vanishes vector zero