Linear Operators: General theory |
From inside the book
Results 1-3 of 87
Page 1
... function f assigns an element f ( a ) e B. If ƒ : A → B and g : B → C , then the mapping gf : A → C is defined by the equation ( gf ) ( a ) = g ( f ( a ) ) for a e A. If f : A → B and CCA , the symbol f ( C ) is used for the set of all ...
... function f assigns an element f ( a ) e B. If ƒ : A → B and g : B → C , then the mapping gf : A → C is defined by the equation ( gf ) ( a ) = g ( f ( a ) ) for a e A. If f : A → B and CCA , the symbol f ( C ) is used for the set of all ...
Page 3
... function f assigns an element ƒ ( a ) e B. If ƒ : A → B and g : B → C , then the mapping gf : A → C is defined by the equation ( gf ) ( a ) g ( f ( a ) ) for a e A. If ƒ : A → B and C CA , the symbol f ( C ) is used for the set of ...
... function f assigns an element ƒ ( a ) e B. If ƒ : A → B and g : B → C , then the mapping gf : A → C is defined by the equation ( gf ) ( a ) g ( f ( a ) ) for a e A. If ƒ : A → B and C CA , the symbol f ( C ) is used for the set of ...
Page 196
... F is a u - measurable function whose values are in L „ ( T , Σr , λ ) , 1 ≤ p < . For each s in S , F ( s ) is an equivalence class of functions , any pair of whose members coincide 2 - almost every- where . If for each s we select a ...
... F is a u - measurable function whose values are in L „ ( T , Σr , λ ) , 1 ≤ p < . For each s in S , F ( s ) is an equivalence class of functions , any pair of whose members coincide 2 - almost every- where . If for each s we select a ...
Contents
B Topological Preliminaries | 10 |
Metric Spaces | 23 |
Product Spaces | 31 |
Copyright | |
49 other sections not shown
Other editions - View all
Common terms and phrases
A₁ Acad additive set function algebra Amer analytic arbitrary B-space B₁ ba(S Banach spaces Borel sets Cauchy sequence compact operator complex numbers contains continuous functions continuous linear converges convex set Corollary countably additive DEFINITION denote dense differential equations Doklady Akad Duke Math E₁ elements ergodic exists extension f₁ function defined function f Hausdorff space Hence Hilbert space homomorphism inequality integral L₁ L₁(S Lebesgue Lemma Let f linear functional linear map linear operator linear topological space measurable functions measure space metric space Nauk SSSR N. S. neighborhood non-negative normed linear space o-field open set operator topology positive measure space Proc PROOF properties proved real numbers reflexive Riesz Russian S₁ scalar semi-group sequentially compact Show subset subspace Suppose theory topological space u-integrable u-measurable u-null uniformly unit sphere valued function vector space weakly compact zero ΕΕΣ