Linear Operators: General theory |
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Page 43
... Boolean algebra is a lattice with unit and zero which is distributive and complemented . Let B be a Boolean algebra , and define multiplication and addi- tion as xy = алу , x + y = ( x ^ y ' ) ( x ' ^ y ) . v лу ) . Then it may be ...
... Boolean algebra is a lattice with unit and zero which is distributive and complemented . Let B be a Boolean algebra , and define multiplication and addi- tion as xy = алу , x + y = ( x ^ y ' ) ( x ' ^ y ) . v лу ) . Then it may be ...
Page 44
... Boolean algebra and x vy = x + y + xy , xy , and x ' 1 + x = хлу = xy . Thus the concepts of Boolean algebra and Boolean ring with unit are equivalent . If B and C are Boolean algebras and h : B → C , then h is said to be a ...
... Boolean algebra and x vy = x + y + xy , xy , and x ' 1 + x = хлу = xy . Thus the concepts of Boolean algebra and Boolean ring with unit are equivalent . If B and C are Boolean algebras and h : B → C , then h is said to be a ...
Page 398
... Boolean algebra is isomorphic ( as a Boolean algebra ) to the Boolean algebra of all open and closed sets of such a space . Such disconnectedness is reflected in the fact that the real space C ( S ) is a complete lattice in the natural ...
... Boolean algebra is isomorphic ( as a Boolean algebra ) to the Boolean algebra of all open and closed sets of such a space . Such disconnectedness is reflected in the fact that the real space C ( S ) is a complete lattice in the natural ...
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