Linear Operators: Spectral theory |
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Page 899
Nelson Dunford, Jacob T. Schwartz. algebra of bounded Borel functions on o ( T ) into the B * -algebra of bound- ed operators in Hilbert space with the property that the functions f ( 2 ) = λ and f ( 2 ) = 1 map into the operators T and ...
Nelson Dunford, Jacob T. Schwartz. algebra of bounded Borel functions on o ( T ) into the B * -algebra of bound- ed operators in Hilbert space with the property that the functions f ( 2 ) = λ and f ( 2 ) = 1 map into the operators T and ...
Page 910
... bounded on the spectrum of T we have , for every a in § and every ɑ , for ... Borel function on σ ( T ) . By hypothesis D , is dense in . We note that if ... bounded Borel functions , i.e. , to L2 ( u ) . An elementary continuity argument ...
... bounded on the spectrum of T we have , for every a in § and every ɑ , for ... Borel function on σ ( T ) . By hypothesis D , is dense in . We note that if ... bounded Borel functions , i.e. , to L2 ( u ) . An elementary continuity argument ...
Page 922
... Borel function defined on the complex plane we have f ( T ) → f ... bounded Borel functions on D. Let B be the B * -algebra , with norm [ f ] = = SUPAED ƒ ( 2 ) , of all complex bounded 922 X. BOUNDED NORMAL OPERATORS IN HILBERT SPACE X.7.1.
... Borel function defined on the complex plane we have f ( T ) → f ... bounded Borel functions on D. Let B be the B * -algebra , with norm [ f ] = = SUPAED ƒ ( 2 ) , of all complex bounded 922 X. BOUNDED NORMAL OPERATORS IN HILBERT SPACE X.7.1.
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