Linear Operators: General theory |
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Page 239
... norm n = 2 = 1 x 00 3. The space is the linear space of all ordered n - tuples [ α1 , .. an of scalars α1 , . , an with the norm = supα . 1≤i≤n 4. The space l , is defined for 1 ≤ p < ∞ as the linear space of all sequences x = { n } ...
... norm n = 2 = 1 x 00 3. The space is the linear space of all ordered n - tuples [ α1 , .. an of scalars α1 , . , an with the norm = supα . 1≤i≤n 4. The space l , is defined for 1 ≤ p < ∞ as the linear space of all sequences x = { n } ...
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 , р > 1 , ( c ) ( Hardy , Littlewood , Polya ) ∞ ( Tf ) ( x ) = f ( y ) max ( x , y ) dy is a map in L , ( 0 , ∞ ) of norm p2 ( p - 1 ) -1 , p > 1 . by 22 Show that the mapping T : { a } → { b } of sequences ...
... norm л ( sin л / р ) −1 , р > 1 , ( c ) ( Hardy , Littlewood , Polya ) ∞ ( Tf ) ( x ) = f ( y ) max ( x , y ) dy is a map in L , ( 0 , ∞ ) of norm p2 ( p - 1 ) -1 , p > 1 . by 22 Show that the mapping T : { a } → { b } of sequences ...
Contents
Exercises | 9 |
Definitions and Basic Properties | 13 |
Metric Spaces | 19 |
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 closed sets compact Hausdorff space compact operator complex numbers contains continuous functions continuous linear converges convex set Corollary countably additive DEFINITION denote dense disjoint Doklady Akad E₁ elements ergodic exists f₁ finite number follows function defined function f Hausdorff space Hence Hilbert space homomorphism 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 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 Theorem theory topological space u-integrable u-measurable u-null uniformly unit sphere vector space weakly compact zero ΕΕΣ