Linear Operators: General theory |
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Page 239
... norm x = supα . 1≤i≤n 4. The space l , is defined for 1 ≤ p < ∞ as the linear space of all sequences x { a } of scalars for which the norm is finite . = 00 00 | x | = { Σ | xn | P } 1 / v n = 1 5. The space is the linear space of ...
... norm x = supα . 1≤i≤n 4. The space l , is defined for 1 ≤ p < ∞ as the linear space of all sequences x { a } of scalars for which the norm is finite . = 00 00 | x | = { Σ | xn | P } 1 / v n = 1 5. The space is the linear space of ...
Page 472
... norm in L ,, p > 1 is strongly differentiable at every point but the origin , and gave conditions for strong differentiability of the norm in the space L1 . He also showed that in the F - space of measurable functions on [ 0 , 1 ] , the ...
... norm in L ,, p > 1 is strongly differentiable at every point but the origin , and gave conditions for strong differentiability of the norm in the space L1 . He also showed that in the F - space of measurable functions on [ 0 , 1 ] , the ...
Page 532
... norm л ( sin л / р ) -1 , p > 1 , ( c ) ( Hardy , Littlewood , Polya ) ( Tf ) ( x ) = So f ( y ) dy 0 max ( x , y ) is a map in L , ( 0 , ∞ ) of norm p2 ( p - 1 ) -1 , p > 1 . → 22 Show that the mapping T : { an } { b } of sequences ...
... norm л ( sin л / р ) -1 , p > 1 , ( c ) ( Hardy , Littlewood , Polya ) ( Tf ) ( x ) = So f ( y ) dy 0 max ( x , y ) is a map in L , ( 0 , ∞ ) of norm p2 ( p - 1 ) -1 , p > 1 . → 22 Show that the mapping T : { an } { b } of sequences ...
Contents
B Topological Preliminaries | 10 |
Metric Spaces | 23 |
Product Spaces | 31 |
Copyright | |
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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 Doklady Akad Duke Math E₁ elements ergodic exists extension f₁ function defined function f Hausdorff space Hence Hilbert space homomorphism inequality integral L₁ L₁(S Lebesgue Lemma Let f linear functional linear map linear operator linear topological space measurable functions measure space metric space Nauk SSSR N. S. neighborhood non-negative normed linear space o-field open set operator topology positive measure space Proc PROOF properties proved real numbers reflexive Riesz Russian S₁ scalar semi-group sequentially compact Show subset subspace Suppose theory topological space u-integrable u-measurable u-null uniformly unit sphere valued function vector space weakly compact zero ΕΕΣ