Linear Operators, Part 2Interscience Publishers, 1963 - Algebra, Universal |
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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 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 ( 7 + 7 ′ ) ) . 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 ( 7 + 7 ′ ) ) . 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
IX | 859 |
Bounded Normal Operators in Hilbert Space | 887 |
Miscellaneous Applications | 937 |
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adjoint extension adjoint operator algebra analytic B-algebra B*-algebra Borel set boundary conditions boundary values bounded operator C₁ closed closure Co(I coefficients compact subset complex numbers continuous function converges Corollary deficiency indices Definition denote dense domain 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 isometric isomorphism kernel L₁(R L₂(I L₂(R Lemma Let f linear linearly independent mapping matrix measure neighborhood norm open set open subset orthonormal partial differential operator Plancherel's theorem positive PROOF prove real axis real numbers satisfies Section sequence solution spectral spectral theory square-integrable subspace Suppose T₁ T₁(t theory To(t topology unique unitary vanishes vector zero