Linear Operators: General theory |
From inside the book
Results 1-3 of 38
Page 106
... S are the functions in the closure TM ( S ) in F ( S ) of the u - simple functions . If for every E in with v ( u , E ) < ∞ , the product Zef of f with the characteristic function ZE of E is totally measurable , the function f is said ...
... S are the functions in the closure TM ( S ) in F ( S ) of the u - simple functions . If for every E in with v ( u , E ) < ∞ , the product Zef of f with the characteristic function ZE of E is totally measurable , the function f is said ...
Page 169
... ( S , Σ , μ ) if and only if for each ɛ > 0 there exists a set E , e Σ and a finite collection of disjoint sets A1 ... TM ( S , E , u ) is complete , so is L1 ( S , Σ , μ ) . 11 Show that if ƒ e L , ( S , Σ , μ ) for some p with 1 ≤ p ...
... ( S , Σ , μ ) if and only if for each ɛ > 0 there exists a set E , e Σ and a finite collection of disjoint sets A1 ... TM ( S , E , u ) is complete , so is L1 ( S , Σ , μ ) . 11 Show that if ƒ e L , ( S , Σ , μ ) for some p with 1 ≤ p ...
Page 329
Nelson Dunford, Jacob T. Schwartz. 11. The Space TM ( S , Σ , μ ) We shall be concerned here with a set S , a o - field Σ of its subsets , and a scalar valued countably additive set function μ on Σ . The symbol TM ( S , E , u ) ... TM(S, Σ,μ)
Nelson Dunford, Jacob T. Schwartz. 11. The Space TM ( S , Σ , μ ) We shall be concerned here with a set S , a o - field Σ of its subsets , and a scalar valued countably additive set function μ on Σ . The symbol TM ( S , E , u ) ... TM(S, Σ,μ)
Contents
A Settheoretic Preliminaries | 1 |
B Topological Preliminaries | 10 |
Algebraic Preliminaries | 34 |
Copyright | |
31 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 disjoint Doklady Akad domain E₁ element exists f₁ finite dimensional finite number function defined function f Hausdorff space Hence Hilbert space homeomorphism inequality integral L₁ L₁(S Lebesgue Lemma Let f linear functional linear map linear operator linear topological space measurable function measure space metric space Nauk SSSR N. S. neighborhood non-negative o-field open set operator topology positive measure space Proc PROOF proved real numbers Riesz Russian S₁ scalar semi-group sequentially compact Show spectral strong operator topology subset subspace Suppose T₁ theory topological space u-integrable u-measurable uniformly unit sphere valued function weakly compact zero ΕΕΣ