Linear Operators: General theory |
From inside the book
Results 1-3 of 75
Page 48
... equivalent to the well - ordering principle ( as in Theorem 2.6 ) is in Hausdorff [ 1 ; p . 140 ] . Zorn [ 1 ] gave a theorem essentially equivalent to Theorem 2.7 . A similar theorem is due to R. L. Moore [ 1 ; p . 84 ] . For proofs of ...
... equivalent to the well - ordering principle ( as in Theorem 2.6 ) is in Hausdorff [ 1 ; p . 140 ] . Zorn [ 1 ] gave a theorem essentially equivalent to Theorem 2.7 . A similar theorem is due to R. L. Moore [ 1 ; p . 84 ] . For proofs of ...
Page 91
... equivalent metric . See also van Dantzig [ 1 ] , [ 2 ] . Norms in linear spaces . We have seen that in a normed ... equivalent invariant metric , but that an F - space may have no bounded sphere . Eidelheit and Mazur [ 1 ] have proved ...
... equivalent metric . See also van Dantzig [ 1 ] , [ 2 ] . Norms in linear spaces . We have seen that in a normed ... equivalent invariant metric , but that an F - space may have no bounded sphere . Eidelheit and Mazur [ 1 ] have proved ...
Page 347
... equivalent to a closed subspace of a space ba ( S , E ) unless both are finite dimen- sional . 51 Show that no space L , ( S , Σ , μ ) , 1 < p < ∞ , is equivalent either to a space C ( S ) or a space L1 ( S1 , E1 , 1 ) , unless it is ...
... equivalent to a closed subspace of a space ba ( S , E ) unless both are finite dimen- sional . 51 Show that no space L , ( S , Σ , μ ) , 1 < p < ∞ , is equivalent either to a space C ( S ) or a space L1 ( S1 , E1 , 1 ) , unless it is ...
Contents
A Settheoretic Preliminaries | 1 |
B Topological Preliminaries | 10 |
Algebraic Preliminaries | 34 |
Copyright | |
31 other sections not shown
Other editions - View all
Common terms and phrases
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