Linear Operators, Part 2Interscience Publishers, 1963 - Algebra, Universal |
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Page 868
... complex number ( M ) such that a + M = x ( M ) e + M . This mapping x → x ( M ) of X into the field of complex numbers is clearly a homomorphism . Since | x ( M ) ≤ x this homo- morphism is continuous . 2 LEMMA . Let u be a non - zero ...
... complex number ( M ) such that a + M = x ( M ) e + M . This mapping x → x ( M ) of X into the field of complex numbers is clearly a homomorphism . Since | x ( M ) ≤ x this homo- morphism is continuous . 2 LEMMA . Let u be a non - zero ...
Page 872
... complex numbers . Thus by Lemma 2 there is a maximal ideal M。 with x ( M 。) = x ( 2 ) for every æ in X. In ... complex plane whose complement is connected . Let C ( o ) be the B - algebra of all continuous complex functions defined on ...
... complex numbers . Thus by Lemma 2 there is a maximal ideal M。 with x ( M 。) = x ( 2 ) for every æ in X. In ... complex plane whose complement is connected . Let C ( o ) be the B - algebra of all continuous complex functions defined on ...
Page 1157
... complex sphere except for a finite number of points , 51 , . . . , Sr lying on the unit circle . Suppose that the coefficients in the Taylor expansion of f in the region || < 1 and the Laurent expansion of f in the region > 1 are ...
... complex sphere except for a finite number of points , 51 , . . . , Sr lying on the unit circle . Suppose that the coefficients in the Taylor expansion of f in the region || < 1 and the Laurent expansion of f in the region > 1 are ...
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