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 XI is an algebra , called the quotient algebra ...
... 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 XI is an algebra , called the quotient algebra ...
Page 44
... algebra and Ꮩ xvy = x + y + xy , xy , and a ' 1 + x 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 ...
... algebra and Ꮩ xvy = x + y + xy , xy , and a ' 1 + x 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 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 B₁ ba(S Banach spaces Borel sets Cauchy sequence compact operator complex numbers contains continuous functions continuous linear converges convex set Corollary countably additive DEFINITION denote dense differential equations disjoint Doklady Akad domain E₁ element exists f₁ finite dimensional finite number function defined function f Hausdorff space Hence Hilbert space homeomorphism inequality integral L₁ L₁(S Lebesgue Lemma Let f linear functional linear map linear operator linear topological space measurable function measure space metric space Nauk SSSR N. S. neighborhood non-negative o-field open set operator topology positive measure space Proc PROOF proved real numbers Riesz Russian S₁ scalar semi-group sequentially compact Show spectral strong operator topology subset subspace Suppose T₁ theory topological space u-integrable u-measurable uniformly unit sphere valued function weakly compact zero ΕΕΣ