Linear Operators: General theory |
From inside the book
Results 1-3 of 79
Page 55
... linear map of X into Y. PROOF . The linearity of T is an immediate consequence of the linearity of the operators T ... linear maps between F - spaces . If lim , Tx exists for each x in a Ꭲ fundamental set , and if for each x in X the ...
... linear map of X into Y. PROOF . The linearity of T is an immediate consequence of the linearity of the operators T ... linear maps between F - spaces . If lim , Tx exists for each x in a Ꭲ fundamental set , and if for each x in X the ...
Page 85
... linear operator mapping & onto Y. The approximation is taken in a sense generalizing the notion of the dif- ferential . This extends theorems of Hildebrandt and Graves [ 1 ] , where the approximating linear ... map of a B - space X onto a B - ...
... linear operator mapping & onto Y. The approximation is taken in a sense generalizing the notion of the dif- ferential . This extends theorems of Hildebrandt and Graves [ 1 ] , where the approximating linear ... map of a B - space X onto a B - ...
Page 490
... linear map from L , [ 0 , 1 ] , p > 1 , to L , [ 0 , 1 ] has the form g ( s ) d S ds Jo 1 K ( s , t ) f ( t ) dt , no satisfactory expression for the norm of T is known . No conditions . on K ( s , t ) are known which are equivalent to ...
... linear map from L , [ 0 , 1 ] , p > 1 , to L , [ 0 , 1 ] has the form g ( s ) d S ds Jo 1 K ( s , t ) f ( t ) dt , no satisfactory expression for the norm of T is known . No conditions . on K ( s , t ) are known which are equivalent to ...
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