Linear Operators, Part 2Interscience Publishers, 1963 - Algebra, Universal |
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Page 906
... unitary if TT * = T * T = I ; it is called self adjoint , symmetric or Hermitian if T = T * ; positive if it is self ... Unitary operators have a number of other characteristic proper- ties . For example , if U is unitary then ( x , y ) ...
... unitary if TT * = T * T = I ; it is called self adjoint , symmetric or Hermitian if T = T * ; positive if it is self ... Unitary operators have a number of other characteristic proper- ties . For example , if U is unitary then ( x , y ) ...
Page 1146
... unitary representations . If such a representation acts in a finite dimensional space E " , then introducing a basis for E " , we may regard the representation as being described by a set of unitary matrices { U1 , ( g ) } . The ...
... unitary representations . If such a representation acts in a finite dimensional space E " , then introducing a basis for E " , we may regard the representation as being described by a set of unitary matrices { U1 , ( g ) } . The ...
Page 1148
... unitary matrices of determinant 1 ; or ( 3 ) The group SpU ( n ) of all 2n x 2n complex unitary matrices V such that [ Vx , Vy ] = [ x , y ] , where [ x , y ] is the non - singular bilinear form [ x , y ] + X2n - 1Y2n - Y2n − 1X2n ; or ...
... unitary matrices of determinant 1 ; or ( 3 ) The group SpU ( n ) of all 2n x 2n complex unitary matrices V such that [ Vx , Vy ] = [ x , y ] , where [ x , y ] is the non - singular bilinear form [ x , y ] + X2n - 1Y2n - Y2n − 1X2n ; or ...
Contents
BAlgebras | 859 |
Commutative BAlgebras | 868 |
Commutative BAlgebras | 874 |
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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 deficiency indices Definition denote dense eigenvalues element equation essential spectrum Exercise 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 L₁(R L₂(I L₂(R Lemma Let f linearly independent mapping matrix measure neighborhood non-zero norm operators in Hilbert orthogonal orthonormal basis Plancherel's theorem positive preceding lemma PROOF prove real axis real numbers satisfies sequence solution spectral spectral theorem square-integrable subspace Suppose T₁ T₂ theory To(t topology tr(T transform unique unitary vanishes vector zero