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Page 73
... s = [ $ 1 , 82 , . . . ] . Show that if the norm of s be defined as [ s ] lub s , 1 < i < ∞ m is a B - space . t ... LIM sn = = 1 , x * ( e ) = 1 , x * ( s ) , show that ∞48 ( a ) LIM sn = LIM Sn + 15 N - ∞ n∞ ( b ) LIM ( as , + ...
... s = [ $ 1 , 82 , . . . ] . Show that if the norm of s be defined as [ s ] lub s , 1 < i < ∞ m is a B - space . t ... LIM sn = = 1 , x * ( e ) = 1 , x * ( s ) , show that ∞48 ( a ) LIM sn = LIM Sn + 15 N - ∞ n∞ ( b ) LIM ( as , + ...
Page 219
... s ) and 00 f ( s ) ds = f ( t ) lim n [ , e - n ( t - s ) f ( s ) ds each holding in the Lebesgue set of f . = f ( t ) , Instead of proving Theorem 10 directly we shall consider in Theorem 11 below the much more general question of when ...
... s ) and 00 f ( s ) ds = f ( t ) lim n [ , e - n ( t - s ) f ( s ) ds each holding in the Lebesgue set of f . = f ( t ) , Instead of proving Theorem 10 directly we shall consider in Theorem 11 below the much more general question of when ...
Page 339
... lim , ( ) , i = 1 , 2 , ... all exist , and that such a sequence con- verges weakly to the element x = { } . Show that if p = 1 , the same condition describes co - convergence in 4 = c * . i - 5 Show that no space B ( S ... ( S ) is weakly ...
... lim , ( ) , i = 1 , 2 , ... all exist , and that such a sequence con- verges weakly to the element x = { } . Show that if p = 1 , the same condition describes co - convergence in 4 = c * . i - 5 Show that no space B ( S ... ( S ) is weakly ...
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