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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 125 , and an orthogonal projection Q in such that Ax = PQx , x = H , P denoting the orthogonal projection of 1 on H. 29 Let { T } be a sequence of bounded operators in ...
... Hilbert space with 0≤ASI be given . Then there exists a Hilbert space 125 , and an orthogonal projection Q in such that Ax = PQx , x = H , P denoting the orthogonal projection of 1 on H. 29 Let { T } be a sequence of bounded operators in ...
Contents
BAlgebras | 859 |
Commutative BAlgebras | 868 |
Commutative BAlgebras | 874 |
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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