Linear Operators, Part 2Interscience Publishers, 1963 - Algebra, Universal |
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Page 898
... Corollary 4 follows immediately from Theorem 1 and Corollary IX.3.15 . Q.E.D. 5 DEFINITION . The uniquely defined spectral measure associat- ed , in Corollary 4 , with the normal operator T is called the resolution of the identity for T ...
... Corollary 4 follows immediately from Theorem 1 and Corollary IX.3.15 . Q.E.D. 5 DEFINITION . The uniquely defined spectral measure associat- ed , in Corollary 4 , with the normal operator T is called the resolution of the identity for T ...
Page 1142
... corollary is obvious . 14 COROLLARY . If A in C , is an operator in the space o of Theorem 5 and ( Aq , q ) = 0 for the characteristic function g of each of the intervals complementary to the set C , then A = nA . Ф PROOF . Let I , be ...
... corollary is obvious . 14 COROLLARY . If A in C , is an operator in the space o of Theorem 5 and ( Aq , q ) = 0 for the characteristic function g of each of the intervals complementary to the set C , then A = nA . Ф PROOF . Let I , be ...
Page 1301
... corollary were false , it would follow that has a boundary value at a which is independent of the set A ,, ... , An - 1 and hence has at least n + 1 independent boundary values at a . But this is impossible by Corollary 22. Q.E.D. 24 ...
... corollary were false , it would follow that has a boundary value at a which is independent of the set A ,, ... , An - 1 and hence has at least n + 1 independent boundary values at a . But this is impossible by Corollary 22. Q.E.D. 24 ...
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