Linear Operators, Part 2Interscience Publishers, 1963 - Algebra, Universal |
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Page 887
Nelson Dunford, Jacob T. Schwartz. CHAPTER X Bounded Normal Operators in Hilbert Space 1. Terminology and Preliminary Notions The spectral theorem to be proved in this chapter will introduce a theory which parallels in Hilbert space the ...
Nelson Dunford, Jacob T. Schwartz. CHAPTER X Bounded Normal Operators in Hilbert Space 1. Terminology and Preliminary Notions The spectral theorem to be proved in this chapter will introduce a theory which parallels in Hilbert space the ...
Page 1025
... Hilbert space . It is desired to generalize the notion of trace to certain operators in Hilbert space and at first glance it may appear that this notion is immediately available for Hilbert - Schmidt operators . However , this is not ...
... Hilbert space . It is desired to generalize the notion of trace to certain operators in Hilbert space and at first glance it may appear that this notion is immediately available for Hilbert - Schmidt operators . However , this is not ...
Page 1262
... Hilbert space with 0 ≤ASI be given . Then there exists a Hilbert space $ 128 , and an orthogonal projection Q in such that Ax = PQx , x = 5 , P denoting the orthogonal projection of H1 on H. 29 Let ... OPERATORS IN HILBERT SPACE XII.9.28.
... Hilbert space with 0 ≤ASI be given . Then there exists a Hilbert space $ 128 , and an orthogonal projection Q in such that Ax = PQx , x = 5 , P denoting the orthogonal projection of H1 on H. 29 Let ... OPERATORS IN HILBERT SPACE XII.9.28.
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