Linear Operators: Spectral theory |
From inside the book
Results 1-3 of 82
Page 885
... topology . PROOF . It is clear from the definition of the centralizer that AC ( A ) and from the lemma that A is closed in the weak operator topology if = ( c ) . To prove the theorem it suffices to show that A if A is closed in the ...
... topology . PROOF . It is clear from the definition of the centralizer that AC ( A ) and from the lemma that A is closed in the weak operator topology if = ( c ) . To prove the theorem it suffices to show that A if A is closed in the ...
Page 922
... topology . If each S , is normal and S is normal then S * → S * in the strong operator topology . PROOF . The first two statements are obvious . The uniform boundedness theorem ( II.3.21 ) yields a constant K with S , ≤K , and thus ...
... topology . If each S , is normal and S is normal then S * → S * in the strong operator topology . PROOF . The first two statements are obvious . The uniform boundedness theorem ( II.3.21 ) yields a constant K with S , ≤K , and thus ...
Page 1921
... topology , definition , VI.1.2 ( 475 ) properties , VI.9.1-5 ( 511 ) , VI.9.11- 12 ( 512-513 ) Strong topology , in a normed space , II.3.1 ( 59 ) , ( 419 ) Structure space of a B - algebra , IX.2.7 ( 869 ) Sturm - Liouville operator ...
... topology , definition , VI.1.2 ( 475 ) properties , VI.9.1-5 ( 511 ) , VI.9.11- 12 ( 512-513 ) Strong topology , in a normed space , II.3.1 ( 59 ) , ( 419 ) Structure space of a B - algebra , IX.2.7 ( 869 ) Sturm - Liouville operator ...
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