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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 ... Normal Operators in Hilbert Space.
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 ... Normal Operators in Hilbert Space.
Page 889
... | x € § , ( T − 2,1 ) x = 0 } of eigenvectors associated with 2 ,. If we define , for every X.1 889 TERMINOLOGY AND PRELIMINARY NOTIONS Terminology and Preliminary Notions The Spectral Theorem for Bounded Normal Operators.
... | x € § , ( T − 2,1 ) x = 0 } of eigenvectors associated with 2 ,. If we define , for every X.1 889 TERMINOLOGY AND PRELIMINARY NOTIONS Terminology and Preliminary Notions The Spectral Theorem for Bounded Normal Operators.
Page 934
... operators in a Hilbert space , then AB is self adjoint . It has been seen ( cf. Exercise X.8.7 ) that if A and B are commuting positive operators , then AB is positive . If A is a normal operator and if B is an operator which commutes ...
... operators in a Hilbert space , then AB is self adjoint . It has been seen ( cf. Exercise X.8.7 ) that if A and B are commuting positive operators , then AB is positive . If A is a normal operator and if B is an operator which commutes ...
Contents
BAlgebras | 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 complex numbers converges Corollary deficiency indices Definition denote dense domain eigenfunctions 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 kernel L₁(R L₂(I L₂(R Lemma Let f linearly independent mapping Math matrix measure neighborhood norm open set operators in Hilbert orthogonal orthonormal partial differential operator Plancherel's theorem positive preceding lemma prove real axis real numbers representation satisfies Section sequence solution spectral spectral theory square-integrable subspace Suppose symmetric operator T₁ T₂ theory To(t topology unique unitary vanishes vector zero