Linear Operators: General theory |
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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 . 22 ... LIM sn = x * ( s ) , show that ( a ) LIM sn LIM Sn + 1 ; - 8 个 N1∞ ( b ) LIM ( as , + ẞtn ) = α LIM sn + ẞ LIM tn ...
... s = [ $ 1 , 82 , . . . ] . Show that if the norm of s be defined as = s lub s , 1 < i < ∞ m is a B - space . 22 ... LIM sn = x * ( s ) , show that ( a ) LIM sn LIM Sn + 1 ; - 8 个 N1∞ ( b ) LIM ( as , + ẞtn ) = α LIM sn + ẞ LIM tn ...
Page 339
... lim „ § ( ” ) , i 1 , 2 , ... all exist , and that such a sequence con- verges weakly to the element a = { } . Show that if p = = 1 , the same condition describes co - convergence in ↳ * - co . 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 a = { } . Show that if p = = 1 , the same condition describes co - convergence in ↳ * - co . 5 Show that no space B ( S ... ( S ) is weakly ...
Page 352
... lim sỗ K ( x , y ) dy = 0 for all 0 < A < ∞ 848 ( d ' ) lim fK ( x , y ) dy = 1 . 848 80 Let k be a non - negative ... ( s ) < ∞ for s > s . Put N ( ƒ , s ) = sõe - stƒ ( t ) μ ( dt ) for s > s 。 and f in Mo. Show that 83 lim N ( s ) ...
... lim sỗ K ( x , y ) dy = 0 for all 0 < A < ∞ 848 ( d ' ) lim fK ( x , y ) dy = 1 . 848 80 Let k be a non - negative ... ( s ) < ∞ for s > s . Put N ( ƒ , s ) = sõe - stƒ ( t ) μ ( dt ) for s > s 。 and f in Mo. Show that 83 lim N ( s ) ...
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