Linear Operators: Spectral theory |
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Page 875
... isomorphism of X onto all of C ( 4 ) . It will also be shown that this isomorphism is a * -isomorphism , i.e. , one preserving the operation of involution . This basic result , which is due to Gelfand and Naĭmark , will find many ...
... isomorphism of X onto all of C ( 4 ) . It will also be shown that this isomorphism is a * -isomorphism , i.e. , one preserving the operation of involution . This basic result , which is due to Gelfand and Naĭmark , will find many ...
Page 878
... isomorphism of B * ( x ) onto C ( ∞ ( x ) ) that we wish to single out . In the notation of the preceding proof the * -isomorphism y↔y ( x ̃1 ( • ) ) of B * ( x ) onto C ( σ ( x ) ) has the property that a corre- sponds to the ...
... isomorphism of B * ( x ) onto C ( ∞ ( x ) ) that we wish to single out . In the notation of the preceding proof the * -isomorphism y↔y ( x ̃1 ( • ) ) of B * ( x ) onto C ( σ ( x ) ) has the property that a corre- sponds to the ...
Page 1355
... isomorphism of E ( A ) L2 ( I ) onto L2 ( 4 , { P1j } ) and that A is an isometric isomorphism of L2 ( 4 , { P } ) onto the subspace L2 ( μ , Ae ; ) of Σ TMTMTM 1L2 ( μ , e¿ ) . = = 1 To prove ( ii ) , note that since G vanishes outside ...
... isomorphism of E ( A ) L2 ( I ) onto L2 ( 4 , { P1j } ) and that A is an isometric isomorphism of L2 ( 4 , { P } ) onto the subspace L2 ( μ , Ae ; ) of Σ TMTMTM 1L2 ( μ , e¿ ) . = = 1 To prove ( ii ) , note that since G vanishes outside ...
Contents
BAlgebras | 859 |
Bounded Normal Operators in Hilbert Space | 887 |
Miscellaneous Applications | 937 |
Copyright | |
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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