Linear Operators: General theory |
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Page 44
... B is a 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 ...
... B is a 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 ...
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 ...
Page 495
... B and if f ( s ) = lim , → ∞ fn ( s ) for every s in S , then fe B. = = It is evident that Bo possesses these two properties . We now prove that Bo is an algebra under the natural product ( fg ) ( s ) f ( s ) g ( s ) , s e S. To see ...
... B and if f ( s ) = lim , → ∞ fn ( s ) for every s in S , then fe B. = = It is evident that Bo possesses these two properties . We now prove that Bo is an algebra under the natural product ( fg ) ( s ) f ( s ) g ( s ) , s e S. To see ...
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