Linear Operators: General theory |
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Page 302
... partial ordering ( I.2.1 ) in L ,. We now establish completeness ( I.12 ) with respect to this ordering . € 2 22 THEOREM . Let ( S , E , μ ) be a positive measure space . Then the real partially ordered space L „ ( S , Σ , μ ) , 1 ≤ p ...
... partial ordering ( I.2.1 ) in L ,. We now establish completeness ( I.12 ) with respect to this ordering . € 2 22 THEOREM . Let ( S , E , μ ) be a positive measure space . Then the real partially ordered space L „ ( S , Σ , μ ) , 1 ≤ p ...
Page 401
... partial differential operators . More detailed indications on this score are given in the section of Notes and Remarks at the end of Chapter XI of Part II . For an account of the principal inequalities connecting Hölder continuous ...
... partial differential operators . More detailed indications on this score are given in the section of Notes and Remarks at the end of Chapter XI of Part II . For an account of the principal inequalities connecting Hölder continuous ...
Page 756
... partial differential equations by the Hahn - Banach Theorem . Trans . Amer . Math . Soc . 76 , 288-299 ( 1954 ) . Gårding , L. 1. Linear hyperbolic partial differential equations with constant coefficients . Acta Math . 85 , 2-62 ( 1950 ) ...
... partial differential equations by the Hahn - Banach Theorem . Trans . Amer . Math . Soc . 76 , 288-299 ( 1954 ) . Gårding , L. 1. Linear hyperbolic partial differential equations with constant coefficients . Acta Math . 85 , 2-62 ( 1950 ) ...
Contents
Preliminary Concepts | 1 |
B Topological Preliminaries | 10 |
Algebraic Preliminaries | 34 |
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A₁ Acad additive set function algebra Amer analytic arbitrary B-space B₁ ba(S Banach spaces Borel sets ca(S Cauchy sequence compact Hausdorff space compact operator complex numbers contains continuous functions converges convex set Corollary countably additive DEFINITION dense disjoint Doklady Akad E₁ element ergodic exists f₁ finite dimensional function defined function f Hausdorff space Hence Hilbert space homeomorphism implies inequality integral isometric isomorphism K₁ L₁ L₁(S Lebesgue Lemma Let f linear manifold linear map linear operator linear topological space measurable functions measure space metric space Nauk SSSR N. S. neighborhood non-negative o-field o-finite open set operator topology positive measure space Proc PROOF properties proved real numbers reflexive Riesz S₁ scalar semi-group sequentially compact Show subset subspace Suppose theory topological space u-integrable u-measurable uniformly weak topology weakly compact weakly sequentially compact zero ΕΕΣ