Linear Operators: General theory |
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Page 412
... linear functional on the vector space X , and let Y be a subspace of X. If f ( Y ) is not the whole field of scalars , then f ( Y ) = 0 . PROOF . Suppose that there exists a ye with f ( y ) 0. Then f ( ay / f ( y ) ) = α , so that every ...
... linear functional on the vector space X , and let Y be a subspace of X. If f ( Y ) is not the whole field of scalars , then f ( Y ) = 0 . PROOF . Suppose that there exists a ye with f ( y ) 0. Then f ( ay / f ( y ) ) = α , so that every ...
Page 418
... linear functional separates K and p . 13 COROLLARY . If p and q are distinct points of a locally convex linear topological space X , there is a continuous linear functional f de- fined on such that f ( p ) f ( q ) . As a last corollary ...
... linear functional separates K and p . 13 COROLLARY . If p and q are distinct points of a locally convex linear topological space X , there is a continuous linear functional f de- fined on such that f ( p ) f ( q ) . As a last corollary ...
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 ...
... 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 ...
Contents
B Topological Preliminaries | 10 |
Metric Spaces | 23 |
Product Spaces | 31 |
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 compact operator complex numbers contains continuous functions continuous linear converges convex set Corollary countably additive DEFINITION denote dense differential equations Doklady Akad Duke Math E₁ elements ergodic exists extension f₁ function defined function f Hausdorff space Hence Hilbert space homomorphism inequality 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 o-field 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 theory topological space u-integrable u-measurable u-null uniformly unit sphere valued function vector space weakly compact zero ΕΕΣ