Linear Operators: General theory |
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Page 237
... Problem . What is an analytical representation of the conjugate space * of the given space X ? 1 2 Problem . When does a sequence { x } in X have the property that the lim x * x , exists for each x * in X * ? 3 Problem . When does a ...
... Problem . What is an analytical representation of the conjugate space * of the given space X ? 1 2 Problem . When does a sequence { x } in X have the property that the lim x * x , exists for each x * in X * ? 3 Problem . When does a ...
Page 756
... problem and the vibration problem for linear elliptic partial differential equations with constant coefficients . Proc . Symposium Spectral Theory and Differential Problems , 291–301 . Oklahoma Agricultural and Mechanical College ...
... problem and the vibration problem for linear elliptic partial differential equations with constant coefficients . Proc . Symposium Spectral Theory and Differential Problems , 291–301 . Oklahoma Agricultural and Mechanical College ...
Page 766
... problem for a finite interval . Bull . Amer . Math . Soc . 38 , 269-270 ( 1932 ) . Convergence of sequences of linear operations . Bull . Amer . Math . Soc . 28 , 53-58 ( 1922 ) . Hildebrandt , T. H. , and Graves , L. M. 1. Implicit ...
... problem for a finite interval . Bull . Amer . Math . Soc . 38 , 269-270 ( 1932 ) . Convergence of sequences of linear operations . Bull . Amer . Math . Soc . 28 , 53-58 ( 1922 ) . Hildebrandt , T. H. , and Graves , L. M. 1. Implicit ...
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