Linear Operators: General theory |
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Page 4
... similar . In particular , if A is a sequence { a } then lim sup A and lim inf A are usually denoted by lim inf an lim sup an n1∞ " ∞4U respectively . If a and b are extended real numbers , then the symbol ( a , b ) denotes the open ...
... similar . In particular , if A is a sequence { a } then lim sup A and lim inf A are usually denoted by lim inf an lim sup an n1∞ " ∞4U respectively . If a and b are extended real numbers , then the symbol ( a , b ) denotes the open ...
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 395
... similar representation theorem can be obtained in which there may be linear relations between the values of the functions at pairs of points . The following result is also due to Kakutani . THEOREM . The conjugate space of an abstract M ...
... similar representation theorem can be obtained in which there may be linear relations between the values of the functions at pairs of points . The following result is also due to Kakutani . THEOREM . The conjugate space of an abstract M ...
Contents
A Settheoretic Preliminaries | 1 |
B Topological Preliminaries | 10 |
Algebraic Preliminaries | 34 |
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A₁ Acad additive set function algebra Amer analytic arbitrary B-space 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 exists f₁ finite dimensional function defined function f g₁ 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-measurable uniformly weak topology weakly compact weakly sequentially compact zero ΕΕΣ