Linear Operators: General theory |
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Page 5
... partially ordered system . An upper bound for a subfamily BCA is any set containing ○ B , and U B is the only least upper bound of B. Similarly , B is the only greatest lower bound ... PARTIALLY ORDERED SYSTEMS Partially Ordered Systems.
... partially ordered system . An upper bound for a subfamily BCA is any set containing ○ B , and U B is the only least upper bound of B. Similarly , B is the only greatest lower bound ... PARTIALLY ORDERED SYSTEMS Partially Ordered Systems.
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 < x ...
... 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 < x ...
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
Exercises | 9 |
Definitions and Basic Properties | 13 |
Metric Spaces | 19 |
Copyright | |
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A₁ Acad additive set function algebra Amer analytic arbitrary B-space B₁ ba(S Banach spaces Borel sets Cauchy sequence closed sets compact Hausdorff space compact operator complex numbers contains continuous functions continuous linear converges convex set Corollary countably additive DEFINITION denote dense disjoint Doklady Akad E₁ elements ergodic exists f₁ finite number follows function defined function f Hausdorff space Hence Hilbert space homomorphism integral L₁ L₁(S Lebesgue Lemma Let f linear functional linear map linear operator linear topological space measurable functions measure space metric space Nauk SSSR N. S. neighborhood non-negative normed linear space open set operator topology positive measure space Proc PROOF properties proved real numbers reflexive Riesz Russian S₁ scalar semi-group sequentially compact Show subset subspace Suppose Theorem theory topological space u-integrable u-measurable u-null uniformly unit sphere vector space weakly compact zero ΕΕΣ