Linear Operators: General theory |
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Page 44
... B is a Boolean algebra and x vy = x + y + xy , xy , and x ' 1 + x = хлу = ху . Thus the concepts of Boolean algebra and Boolean ring with unit are equivalent . If B and C are Boolean algebras and h : BC , then h is said to be a ...
... B is a Boolean algebra and x vy = x + y + xy , xy , and x ' 1 + x = хлу = ху . Thus the concepts of Boolean algebra and Boolean ring with unit are equivalent . If B and C are Boolean algebras and h : BC , then h is said to be a ...
Page 396
... algebra , norm and order properties . Further results based only on algebra and norm properties were developed by Gelfand [ 1 ] in the complex case and were ... algebraic considerations are for 396 IV.16 IV . SPECIAL SPACES B-Algebras.
... algebra , norm and order properties . Further results based only on algebra and norm properties were developed by Gelfand [ 1 ] in the complex case and were ... algebraic considerations are for 396 IV.16 IV . SPECIAL SPACES B-Algebras.
Page 397
... B - algebra is the space of quaternion valued continuous functions on a compact Hausdorff space . Characterization on the basis of order and linear properties were made by Fan [ 2 ] and Kadison [ 1 ] . Kadison's work is sufficiently ...
... B - algebra is the space of quaternion valued continuous functions on a compact Hausdorff space . Characterization on the basis of order and linear properties were made by Fan [ 2 ] and Kadison [ 1 ] . Kadison's work is sufficiently ...
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