Linear Operators, Part 2Interscience Publishers, 1963 - Algebra, Universal |
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Page 1094
... inequality by the elementary inequality \ x \ ” + | y | ” ≥ \ x + y ” , valid in this range of p . Similarly , using Corollary 3 , and the Hölder inequality α . valid if r11 + r21 = r1 and 0 < r1 , r2 , r < ∞o , we obtain ( c ) ...
... inequality by the elementary inequality \ x \ ” + | y | ” ≥ \ x + y ” , valid in this range of p . Similarly , using Corollary 3 , and the Hölder inequality α . valid if r11 + r21 = r1 and 0 < r1 , r2 , r < ∞o , we obtain ( c ) ...
Page 1105
... inequality ( a ) for operators in a d - dimensional Hilbert space . Arguing as in the paragraphs of the proof of Lemma 14 following formula ( 3 ) of that proof , where we proved a bilinear inequality quite similar to our present ...
... inequality ( a ) for operators in a d - dimensional Hilbert space . Arguing as in the paragraphs of the proof of Lemma 14 following formula ( 3 ) of that proof , where we proved a bilinear inequality quite similar to our present ...
Page 1774
... inequality , known as the Schwarz inequality , will be proved first . It follows from the postulates for that the Schwarz inequality is valid if either x or y is zero . Hence suppose that x0y . For an arbitrary complex number & 0 ≤ ( x ...
... inequality , known as the Schwarz inequality , will be proved first . It follows from the postulates for that the Schwarz inequality is valid if either x or y is zero . Hence suppose that x0y . For an arbitrary complex number & 0 ≤ ( x ...
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