Linear Operators: General theory |
From inside the book
Results 1-3 of 71
Page 237
... Problem . What is an analytical representation of the conjugate * of the given space X ? space 1 2 Problem . When does a sequence { x } in X have the property that the lim x * x , exists for each a * in X * ? 3 Problem . When does a ...
... Problem . What is an analytical representation of the conjugate * of the given space X ? space 1 2 Problem . When does a sequence { x } in X have the property that the lim x * x , exists for each a * in X * ? 3 Problem . When does a ...
Page 613
... problem is to determine the most general continuous operator valued functions defined on the range t≥0 , which satisfy the equations ( i ) T ( t + u ) = T ( t ) T ( u ) , T ( 0 ) = 1 , t , u ≥ 0 . An operator valued function T ( t ) ...
... problem is to determine the most general continuous operator valued functions defined on the range t≥0 , which satisfy the equations ( i ) T ( t + u ) = T ( t ) T ( u ) , T ( 0 ) = 1 , t , u ≥ 0 . An operator valued function T ( t ) ...
Page 658
... problem of determining whether or not the limit ( iii ) exists . The next four sections are devoted to a study of this problem and various of its generalizations which arise in the theory of stochastic processes . It should be observed ...
... problem of determining whether or not the limit ( iii ) exists . The next four sections are devoted to a study of this problem and various of its generalizations which arise in the theory of stochastic processes . It should be observed ...
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