Linear Operators: General theory |
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Page 51
... linear topological space . Then the denumerable set of vectors of the form ax + ... + ẞy with a , Po and x ... linear topological space X is bounded if , given any neighborhood V of the zero in X , there exists a positive real number ...
... linear topological space . Then the denumerable set of vectors of the form ax + ... + ẞy with a , Po and x ... linear topological space X is bounded if , given any neighborhood V of the zero in X , there exists a positive real number ...
Page 419
... topology of X. The following lemma is a consequence of Definition 2 . 3 LEMMA . If I is a total linear space of linear functionals on X , X is a locally convex linear topological space in its I topology . Note that may already be a linear ...
... topology of X. The following lemma is a consequence of Definition 2 . 3 LEMMA . If I is a total linear space of linear functionals on X , X is a locally convex linear topological space in its I topology . Note that may already be a linear ...
Page 436
... linear vector space . Show that X is a total space of linear functionals on X. 2 If X is an infinite dimensional B - space then X * # X * . 3 Let X be a linear topological space . Then X has a non - zero continuous linear functional if ...
... linear vector space . Show that X is a total space of linear functionals on X. 2 If X is an infinite dimensional B - space then X * # X * . 3 Let X be a linear topological space . Then X has a non - zero continuous linear functional if ...
Contents
Preliminary Concepts | 1 |
B Topological Preliminaries | 10 |
Algebraic Preliminaries | 34 |
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A₁ Acad additive set function algebra Amer analytic arbitrary B-space B₁ ba(S Banach spaces Borel sets ca(S Cauchy sequence compact Hausdorff space compact operator complex numbers contains continuous functions converges convex set Corollary countably additive DEFINITION dense disjoint Doklady Akad E₁ element ergodic exists f₁ finite dimensional function defined function f Hausdorff space Hence Hilbert space homeomorphism implies inequality integral isometric isomorphism K₁ L₁ L₁(S Lebesgue Lemma Let f linear manifold linear map linear operator linear topological space measurable functions measure space metric space Nauk SSSR N. S. neighborhood non-negative o-field o-finite open set operator topology positive measure space Proc PROOF properties proved real numbers reflexive Riesz S₁ scalar semi-group sequentially compact Show subset subspace Suppose theory topological space u-integrable u-measurable uniformly weak topology weakly compact weakly sequentially compact zero ΕΕΣ