Linear Operators: General theory |
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Page 84
... Similar theorems may be proved in more general topological spaces , which do not necessarily have a group structure . For instance , Dunford [ 5 ] generalized the notion of category to derive conditions which are sufficient that a one ...
... Similar theorems may be proved in more general topological spaces , which do not necessarily have a group structure . For instance , Dunford [ 5 ] generalized the notion of category to derive conditions which are sufficient that a one ...
Page 463
... similar vein , Krein and Smulian [ 1 ] introduced a definition of a regularly convex set in X * . It is not difficult to establish that the regularly convex sets in X * are merely the convex sets which are closed in the X topology of X ...
... similar vein , Krein and Smulian [ 1 ] introduced a definition of a regularly convex set in X * . It is not difficult to establish that the regularly convex sets in X * are merely the convex sets which are closed in the X topology of X ...
Page 541
... similar example was given by Yosida , Mimura and Kakutani [ 1 ] . If S is Euclidean , Dunford and Pettis [ 1 ] showed that the square of any weakly compact operator in L1 ( S ) is strongly compact . This was proved for a measure space ...
... similar example was given by Yosida , Mimura and Kakutani [ 1 ] . If S is Euclidean , Dunford and Pettis [ 1 ] showed that the square of any weakly compact operator in L1 ( S ) is strongly compact . This was proved for a measure space ...
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