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 xvy = x + y + xy , xy , and x ' 1 + x x λ y = 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 ...
... algebra and xvy = x + y + xy , xy , and x ' 1 + x x λ y = 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 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 continuous linear converges convex set Corollary countably additive DEFINITION disjoint Doklady Akad E₁ element exists f₁ finite dimensional function defined function f Hausdorff space Hence Hilbert space integral isometric isomorphism K₁ L₁ L₁(S Lebesgue Lemma Let f linear functional 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 Russian S₁ scalar semi-group sequentially compact Show subset subspace Suppose theory TM(S topological space u-integrable u-measurable uniformly weak topology weakly compact weakly sequentially compact zero ΕΕΣ