Linear Operators, Part 2Interscience Publishers, 1963 - Algebra, Universal |
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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 $ , 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 $ , the centralizer ( 884 IX.5 IX . B - ALGEBRAS.
Page 1156
... result , which is dual to Theorem 8 . 9 THEOREM . If R is a discrete Abelian group , its character group R is compact . The results of Sections 3 and 4 carry over for the case of discrete groups and many of them , for example Theorem ...
... result , which is dual to Theorem 8 . 9 THEOREM . If R is a discrete Abelian group , its character group R is compact . The results of Sections 3 and 4 carry over for the case of discrete groups and many of them , for example Theorem ...
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 |
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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