Linear Operators: General theory |
From inside the book
Results 1-3 of 87
Page 14
... topology in the set of scalars is always assumed to be that determined by the base whose elements are neighborhoods of the form { B | B — α < ε } . --- 18 LEMMA . Let f , g be continuous scalar functions on a topological space X , and ...
... topology in the set of scalars is always assumed to be that determined by the base whose elements are neighborhoods of the form { B | B — α < ε } . --- 18 LEMMA . Let f , g be continuous scalar functions on a topological space X , and ...
Page 51
... topological space X is bounded if , given any neighborhood V of the zero in X , there exists a positive real number & such that BC V providing a ε . 8 LEMMA . A compact subset of a linear topological space is bounded . PROOF . Let B be ...
... topological space X is bounded if , given any neighborhood V of the zero in X , there exists a positive real number & such that BC V providing a ε . 8 LEMMA . A compact subset of a linear topological space is bounded . PROOF . Let B be ...
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 ...
... 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 ...
Contents
Preliminary Concepts | 1 |
B Topological Preliminaries | 10 |
Algebraic Preliminaries | 34 |
Copyright | |
80 other sections not shown
Other editions - View all
Common terms and phrases
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