Linear Operators: General theory |
From inside the book
Results 1-3 of 78
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 , Σ ) 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 , Σ ) 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 ...
Page 663
... equivalent functions , it is seen that T may not be regarded as being defined on L , ( S , Σ , μ ) unless ƒ ( p ( s ) ... equivalent functions into μ - equivalent functions . Furthermore T is a continuous linear map of the F - space M ( S ) ...
... equivalent functions , it is seen that T may not be regarded as being defined on L , ( S , Σ , μ ) unless ƒ ( p ( s ) ... equivalent functions into μ - equivalent functions . Furthermore T is a continuous linear map of the F - space M ( S ) ...
Contents
A Settheoretic Preliminaries | 1 |
10 | 30 |
Three Basic Principles of Linear Analysis | 49 |
Copyright | |
31 other sections not shown
Other editions - View all
Common terms and phrases
A₁ additive set function algebra analytic arbitrary B-space B₁ ba(S Banach Borel sets ca(S Cauchy sequence closed unit sphere compact Hausdorff space compact operator complex numbers conditionally compact contains continuous functions convex set Corollary countably additive DEFINITION denote dense E₁ element equation equivalent exists f₁ finite dimensional function defined function f Hausdorff space Hence Hilbert space homeomorphism implies inequality integral isometric isomorphism K₁ L₁ L₁(S Lebesgue measure Lemma Let f linear map linear operator linear topological space Math measurable functions measure space metric space neighborhood non-negative non-zero normed linear space o-field o-finite open set operator topology positive measure space properties proved real numbers reflexive Riesz S₁ scalar semi-group sequentially compact Show subset subspace Suppose theory TM(S topological space u-integrable u-measurable uniformly valued function weak topology weakly compact weakly sequentially compact X₁ zero ΕΕΣ