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 . 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 . 22 THEOREM . Let ( S , E , μ ) be a positive measure space . Then the real partially ordered space L , ( S , Σ , μ ) , 1 ≤ p ...
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 ) ...
Page 819
... partially ordered spaces . Doklady Akad . Nauk SSSR ( N. S. ) 58 , 733–736 ( 1947 ) . ( Russian ) Math . Rev. 9 , 290 ( 1948 ) . The product in linear partially ordered spaces and its application to the theory of operations , I. Mat ...
... partially ordered spaces . Doklady Akad . Nauk SSSR ( N. S. ) 58 , 733–736 ( 1947 ) . ( Russian ) Math . Rev. 9 , 290 ( 1948 ) . The product in linear partially ordered spaces and its application to the theory of operations , I. Mat ...
Contents
A Settheoretic Preliminaries | 1 |
B Topological Preliminaries | 10 |
Algebraic Preliminaries | 34 |
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A₁ Acad additive set function algebra Amer analytic arbitrary B-space 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 exists f₁ finite dimensional function defined function f g₁ 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-measurable uniformly weak topology weakly compact weakly sequentially compact zero ΕΕΣ