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'Ʌy ) . \ Then it may be verified that ...
... 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'Ʌy ) . \ Then it may be verified that ...
Page 44
... Boolean algebra and xvy = x + y + xy , 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 homomorphism , or a Boolean ...
... Boolean algebra and xvy = x + y + xy , 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 homomorphism , or a Boolean ...
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
Exercises | 9 |
Definitions and Basic Properties | 13 |
Metric Spaces | 19 |
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 closed sets compact Hausdorff space compact operator complex numbers contains continuous functions continuous linear converges convex set Corollary countably additive DEFINITION denote dense disjoint Doklady Akad E₁ elements ergodic exists f₁ finite number follows function defined function f Hausdorff space Hence Hilbert space homomorphism 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 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 Theorem theory topological space u-integrable u-measurable u-null uniformly unit sphere vector space weakly compact zero ΕΕΣ