Linear Operators: General theory |
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Page 539
... Representation of operators in C. The representation of the general operator with domain and range in C [ 0 , 1 ] was given by Radon [ 1 ] . Both C. Fischer [ 1 ] and Radon [ 1 ] treated the compact operator from C [ 0 , 1 ] to itself ...
... Representation of operators in C. The representation of the general operator with domain and range in C [ 0 , 1 ] was given by Radon [ 1 ] . Both C. Fischer [ 1 ] and Radon [ 1 ] treated the compact operator from C [ 0 , 1 ] to itself ...
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 4 ( a ) 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 ...
... representation of the vector 4 ( a ) 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 ...
Contents
Preliminary Concepts | 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 ca(S Cauchy sequence compact Hausdorff space compact operator complex numbers contains continuous functions converges convex set Corollary countably additive DEFINITION dense disjoint Doklady Akad E₁ element ergodic exists f₁ finite dimensional function defined function f Hausdorff space Hence Hilbert space homeomorphism implies inequality integral isometric isomorphism K₁ L₁ L₁(S Lebesgue Lemma Let f linear manifold linear map linear operator linear topological space measurable functions measure space metric space Nauk SSSR N. S. neighborhood non-negative o-field o-finite open set operator topology positive measure space Proc PROOF properties proved real numbers reflexive Riesz S₁ scalar semi-group sequentially compact Show subset subspace Suppose theory topological space u-integrable u-measurable uniformly weak topology weakly compact weakly sequentially compact zero ΕΕΣ