Linear Operators: General theory |
From inside the book
Results 1-3 of 75
Page 542
... representations were given in Sections 7-8 . For the convenience of the reader , we have tabulated here references to the literature where such representation theorems are explicitly stated . There are four tables ; one for the general ...
... representations were given in Sections 7-8 . For the convenience of the reader , we have tabulated here references to the literature where such representation theorems are explicitly stated . There are four tables ; one for the general ...
Page 686
... representation of the vector A ( x ) f in L ,. If we had started with another [ t , s ] -measurable representation K ( t , s ) of T ( t ) f then , since for almost all s , K ( t , s ) T ( t ) ( f , s ) for almost all t , it is seen that ...
... representation of the vector A ( x ) f in L ,. If we had started with another [ t , s ] -measurable representation K ( t , s ) of T ( t ) f then , since for almost all s , K ( t , s ) T ( t ) ( f , s ) for almost all t , it is seen that ...
Page 733
... Representation of functionals by integrals . Duke Math . J. 17 , 499–506 ( 1950 ) . 4. Approximation in , and representation of , certain Banach algebras . Amer . J. Math . 71 , 763-790 ( 1949 ) . 5 . 6 . A topology for spaces of ...
... Representation of functionals by integrals . Duke Math . J. 17 , 499–506 ( 1950 ) . 4. Approximation in , and representation of , certain Banach algebras . Amer . J. Math . 71 , 763-790 ( 1949 ) . 5 . 6 . A topology for spaces of ...
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