Linear Operators: General theory |
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Page 58
... linear , and continuous ( I.8.3 ) . Hence , by Theorem 2 . its inverse pr1 is continuous . Thus T = propr1 is continuous ( I.4.17 ) . Q.E.D. 5 THEOREM . If a linear space is an F - space under each of two metrics , and if one of the ...
... linear , and continuous ( I.8.3 ) . Hence , by Theorem 2 . its inverse pr1 is continuous . Thus T = propr1 is continuous ( I.4.17 ) . Q.E.D. 5 THEOREM . If a linear space is an F - space under each of two metrics , and if one of the ...
Page 452
... linear topological space X , and K X , then there exists a non- zero continuous linear functional tangent to K at p . If A is a subset of X , and p is in A , then there exists a non - zero continuous linear functional tangent to A at p ...
... linear topological space X , and K X , then there exists a non- zero continuous linear functional tangent to K at p . If A is a subset of X , and p is in A , then there exists a non - zero continuous linear functional tangent to A at p ...
Page 513
... continuous with the topology in Y * and the X topology in X * , then there exists a bounded linear operator T : X →→ Y such that T * = U. - > 14 Let T be a linear , but not necessarily continuous , mapping between B - space X and Y ...
... continuous with the topology in Y * and the X topology in X * , then there exists a bounded linear operator T : X →→ Y such that T * = U. - > 14 Let T be a linear , but not necessarily continuous , mapping between B - space X and Y ...
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