Linear Operators, Part 2Interscience Publishers, 1963 - Algebra, Universal |
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Page 868
... complex number x ( M ) such that x + M = x ( M ) e + M . This mapping x → x ( M ) of X into the field Ø of complex numbers is clearly a homomorphism . Since ( M ) | ≤ | x | this homo- morphism is continuous . 2 LEMMA . Let μ be a non ...
... complex number x ( M ) such that x + M = x ( M ) e + M . This mapping x → x ( M ) of X into the field Ø of complex numbers is clearly a homomorphism . Since ( M ) | ≤ | x | this homo- morphism is continuous . 2 LEMMA . Let μ be a non ...
Page 872
... complex plane whose complement is connected . Let C ( σ ) be the B - algebra of all continuous complex functions defined on σ with norm = 1/1 = sup | f ( 2 ) . λεσ = Let z be the element in C ( o ) with z ( 2 ) = 2 , 2 € σ , and let Xo ...
... complex plane whose complement is connected . Let C ( σ ) be the B - algebra of all continuous complex functions defined on σ with norm = 1/1 = sup | f ( 2 ) . λεσ = Let z be the element in C ( o ) with z ( 2 ) = 2 , 2 € σ , and let Xo ...
Page 1156
... complex numbers of unit modulus . Using the second of these realizations for R we have [ n , λ ] = 2 " where n e R ... complex numbers . Let f be the function of the complex variable z defined by 10 f ( z ) = ∞ Σαμπ " , n = 1 ∞ - Σα ...
... complex numbers of unit modulus . Using the second of these realizations for R we have [ n , λ ] = 2 " where n e R ... complex numbers . Let f be the function of the complex variable z defined by 10 f ( z ) = ∞ Σαμπ " , n = 1 ∞ - Σα ...
Contents
BAlgebras | 859 |
Commutative BAlgebras | 868 |
Commutative BAlgebras | 874 |
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Acad adjoint extension adjoint operator algebra Amer analytic B-algebra B*-algebra Banach Banach spaces Borel set boundary conditions boundary values bounded operator C₁ closed closure Co(I coefficients complex numbers continuous function converges Corollary deficiency indices Definition denote dense differential equations Doklady Akad domain eigenfunctions eigenvalues element essential spectrum exists follows from Lemma follows immediately formal differential operator formally self adjoint formula 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 linearly independent mapping Math matrix measure Nauk SSSR N. S. neighborhood norm open set operators in Hilbert orthogonal orthonormal positive Proc PROOF prove real axis satisfies sequence singular solution spectral spectral theory square-integrable subspace Suppose T₁ T₂ theory To(t topology transform unique unitary vanishes vector zero