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 μ be a non ...
... 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 μ be a non ...
Page 872
... complex numbers . Thus by Lemma 2 there is a maximal ideal Mo with x ( Mo ) = x ( 2 ) for every a in X. In ... complex plane whose complement is connected . Let C ( o ) be the B - algebra of all continuous complex functions defined on σ ...
... complex numbers . Thus by Lemma 2 there is a maximal ideal Mo with x ( Mo ) = x ( 2 ) for every a in X. In ... complex plane whose complement is connected . Let C ( o ) be the B - algebra of all continuous complex functions defined on σ ...
Page 1157
... complex sphere except for a finite number of points , 51 , ... , 5 , lying on the unit circle . Suppose that the coefficients in the Taylor expansion of f in the region | z | < 1 and the Laurent expansion of f in the region z > 1 are ...
... complex sphere except for a finite number of points , 51 , ... , 5 , lying on the unit circle . Suppose that the coefficients in the Taylor expansion of f in the region | z | < 1 and the Laurent expansion of f in the region z > 1 are ...
Contents
IX | 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 compact subset complex numbers continuous function converges Corollary deficiency indices Definition denote dense domain 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 isometric isomorphism kernel L₁(R L₂(I L₂(R Lemma Let f linear linearly independent mapping matrix measure neighborhood norm open set open subset orthonormal partial differential operator Plancherel's theorem positive PROOF prove real axis real numbers satisfies Section sequence solution spectral spectral theory square-integrable subspace Suppose T₁ T₁(t theory To(t topology unique unitary vanishes vector zero