Linear Operators: General theory |
From inside the book
Results 1-3 of 44
Page 20
... sequence { a } is said to be convergent if ana for some a . A sequence { a } in a metric space is a Cauchy sequence if limm , n o ( am , an ) = 0. If every Cauchy se- quence is convergent , a metric space is said to be complete . The ...
... sequence { a } is said to be convergent if ana for some a . A sequence { a } in a metric space is a Cauchy sequence if limm , n o ( am , an ) = 0. If every Cauchy se- quence is convergent , a metric space is said to be complete . The ...
Page 68
... Cauchy sequence of scalars for each a * € X * is called a weak Cauchy sequence . The space X is said to be weakly complete if every weak Cauchy sequence has a weak limit . In Chapter V , a topology is introduced in certain linear spaces ...
... Cauchy sequence of scalars for each a * € X * is called a weak Cauchy sequence . The space X is said to be weakly complete if every weak Cauchy sequence has a weak limit . In Chapter V , a topology is introduced in certain linear spaces ...
Page 122
... sequence of functions in L ( S , E , μ , X ) and let f be a function on S to X. Then f is in L , and \ ƒnƒ ... Cauchy sequence in L1 ( S ) . For ε > 0 there is , by ( iii ) , a set E with v ( μ , E ) < ∞ such that 8 \ En − 6m \ 1 ≤ 28 ...
... sequence of functions in L ( S , E , μ , X ) and let f be a function on S to X. Then f is in L , and \ ƒnƒ ... Cauchy sequence in L1 ( S ) . For ε > 0 there is , by ( iii ) , a set E with v ( μ , E ) < ∞ such that 8 \ En − 6m \ 1 ≤ 28 ...
Contents
8 | 28 |
Algebraic Preliminaries | 34 |
Three Basic Principles of Linear Analysis | 49 |
Copyright | |
40 other sections not shown
Other editions - View all
Common terms and phrases
A₁ additive set function algebra Amer analytic arbitrary B-space ba(S Banach Borel sets ca(S Cauchy sequence compact Hausdorff space compact operator complex numbers contains continuous functions converges convex set Corollary countably additive DEFINITION dense differential disjoint Doklady Akad E₁ element equation exists f₁ finite dimensional function defined function f Hausdorff space Hence Hilbert space homeomorphism implies inequality integral isometric isomorphism L₁ L₁(S Lebesgue Lemma Let f linear map linear operator linear topological space Math measurable functions measure space metric space Nauk SSSR N. S. neighborhood non-negative normed linear space o-field o-finite open set operator topology positive measure space Proc PROOF properties proved real numbers Riesz S₁ scalar semi-group sequentially compact Show subset subspace Suppose theory TM(S topological space u-integrable u-measurable uniformly weak topology weakly compact weakly sequentially compact zero ΕΕΣ