Linear Operators: Spectral theory |
From inside the book
Results 1-3 of 87
Page 922
... topology . Then Sn + Tn → S + T , aSaS , and ST , ST in the strong operator topology . If each S , is normal and S is normal then S →→ S * in the strong S * operator topology . n PROOF . The first two statements are obvious . The ...
... topology . Then Sn + Tn → S + T , aSaS , and ST , ST in the strong operator topology . If each S , is normal and S is normal then S →→ S * in the strong S * operator topology . n PROOF . The first two statements are obvious . The ...
Page 1420
... topology of the Hilbert space D ( T1 ( t ) ) is the same as its relative topology as a subspace of the Hilbert space D ( T1 ( T + T ' ) ) . Indeed , let { f } be a sequence in D ( T1 ( T ) ) . Suppose that { f } converges to zero in the ...
... topology of the Hilbert space D ( T1 ( t ) ) is the same as its relative topology as a subspace of the Hilbert space D ( T1 ( T + T ' ) ) . Indeed , let { f } be a sequence in D ( T1 ( T ) ) . Suppose that { f } converges to zero in the ...
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 |
Commutative BAlgebras | 868 |
Commutative BAlgebras | 874 |
Copyright | |
45 other sections not shown
Other editions - View all
Common terms and phrases
A₁ 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 countably deficiency indices Definition denote dense eigenfunctions eigenvalues element equation essential spectrum Exercise exists f₁ finite dimensional follows from Lemma follows from Theorem formal differential operator formally self adjoint formula Fourier function f Haar measure Hence Hilbert space Hilbert-Schmidt operator homomorphism identity inequality infinity integral interval kernel L₁ L₁(R L₂ L₂(I L₂(R Lemma Let f linearly independent mapping matrix measure neighborhood non-zero norm operators in Hilbert orthogonal Plancherel's theorem positive preceding lemma prove real axis real numbers satisfies sequence shows solution spectral set spectral theorem square-integrable subset subspace Suppose T₁ T₂ theory To(t topology tr(T transform uniformly unique unitary vanishes vector zero