Linear Operators: General theory |
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Page 73
... s = [ S1 , S2 , . . . ] . Show that if the norm of s be defined as m is a B - space . = [ s ] lub s 1≤i < ∞ 22 ... LIM Sn ( a ) LIM S 0446 = LIM Sn + 1 ; ∞48 ( b ) LIM ( asn + ẞtn ) ∞48 n1∞ [ S1 , S2 , ... ] is an element of m ...
... s = [ S1 , S2 , . . . ] . Show that if the norm of s be defined as m is a B - space . = [ s ] lub s 1≤i < ∞ 22 ... LIM Sn ( a ) LIM S 0446 = LIM Sn + 1 ; ∞48 ( b ) LIM ( asn + ẞtn ) ∞48 n1∞ [ S1 , S2 , ... ] is an element of m ...
Page 219
Nelson Dunford, Jacob T. Schwartz. lim and [ ∞ sin2n ( t - s ) 00 n ( t - s ) f ( s ) ds = f ( t ) lim n ( R e - n ( t - s ) f ( s ) ds = f ( t ) , 8 个» each holding in the Lebesgue set of f . Instead of proving Theorem 10 directly we ...
Nelson Dunford, Jacob T. Schwartz. lim and [ ∞ sin2n ( t - s ) 00 n ( t - s ) f ( s ) ds = f ( t ) lim n ( R e - n ( t - s ) f ( s ) ds = f ( t ) , 8 个» each holding in the Lebesgue set of f . Instead of proving Theorem 10 directly we ...
Page 339
... lim , § ) , i all exist , and that such a sequence con- 1 , 2 , verges weakly to the element a = i = .... = { } . Show that if p condition describes co - convergence in = c * . = = 1 , the same 5 Show that no space B ( S ... ( S ) is weakly ...
... lim , § ) , i all exist , and that such a sequence con- 1 , 2 , verges weakly to the element a = i = .... = { } . Show that if p condition describes co - convergence in = c * . = = 1 , the same 5 Show that no space B ( S ... ( S ) is weakly ...
Contents
8 | 28 |
Algebraic Preliminaries | 34 |
Three Basic Principles of Linear Analysis | 49 |
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A₁ additive set function algebra Amer analytic arbitrary B-space ba(S Banach Borel sets ca(S Cauchy sequence compact Hausdorff space compact operator complex numbers contains continuous functions converges convex set Corollary countably additive DEFINITION dense differential disjoint Doklady Akad E₁ element equation exists f₁ finite dimensional function defined function f Hausdorff space Hence Hilbert space homeomorphism implies inequality integral isometric isomorphism L₁ L₁(S Lebesgue Lemma Let f linear map linear operator linear topological space Math measurable functions measure space metric space Nauk SSSR N. S. neighborhood non-negative normed linear space o-field o-finite open set operator topology positive measure space Proc PROOF properties proved real numbers Riesz 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