Linear Operators: General theory |
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Page 40
... algebra is a right ( left , two - sided ) ideal in the ring sense which is also closed under multiplication by scalars . If I is a two - sided ideal in an algebra X then the quotient ring X / I is an algebra , called the quotient ...
... algebra is a right ( left , two - sided ) ideal in the ring sense which is also closed under multiplication by scalars . If I is a two - sided ideal in an algebra X then the quotient ring X / I is an algebra , called the quotient ...
Page 44
... 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 homomorphism , or a ...
... 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 homomorphism , or a ...
Page 272
... algebra . One of these properties is a well known approximation theo- rem of Weierstrass , which asserts that a ... algebra , for if ƒ and g are in C ( S ) , then the product fg , defined by ( fg ) ( s ) = f ( s ) g ( s ) , is also in C ...
... algebra . One of these properties is a well known approximation theo- rem of Weierstrass , which asserts that a ... algebra , for if ƒ and g are in C ( S ) , then the product fg , defined by ( fg ) ( s ) = f ( s ) g ( s ) , is also in C ...
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