Linear Operators: General theory |
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Page 239
... norm .. n x = = 00 i = 1 3. The space 1 is the linear space of all ordered n - tuples [ α1 , ... , an ] of scalars a1 , ... , an with the norm | xc | = sup . 1≤i≤n 4. The space l , is defined for 1 ≤ p < ∞ as the linear space of all ...
... norm .. n x = = 00 i = 1 3. The space 1 is the linear space of all ordered n - tuples [ α1 , ... , an ] of scalars a1 , ... , an with the norm | xc | = sup . 1≤i≤n 4. The space l , is defined for 1 ≤ p < ∞ as the linear space of all ...
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 ) = So f ( y ) dy max ( x , y ) 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 ) = So f ( y ) dy max ( x , y ) 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
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