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 xv y = x + y + xy , xy , and x ' хлу = xy . 1 + x 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 xv y = x + y + xy , xy , and x ' хлу = xy . 1 + x 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 |
10 | 30 |
Three Basic Principles of Linear Analysis | 49 |
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A₁ additive set function algebra analytic arbitrary B-space B₁ ba(S Banach Borel sets ca(S Cauchy sequence closed unit sphere compact Hausdorff space compact operator complex numbers conditionally compact contains continuous functions convex set Corollary countably additive DEFINITION denote dense E₁ element equation equivalent exists f₁ finite dimensional function defined function f Hausdorff space Hence Hilbert space homeomorphism implies inequality integral isometric isomorphism K₁ L₁ L₁(S Lebesgue measure Lemma Let f linear map linear operator linear topological space Math measurable functions measure space metric space neighborhood non-negative non-zero normed linear space o-field o-finite open set operator topology positive measure space properties proved real numbers reflexive Riesz S₁ scalar semi-group sequentially compact Show subset subspace Suppose theory TM(S topological space u-integrable u-measurable uniformly valued function weak topology weakly compact weakly sequentially compact X₁ zero ΕΕΣ