Linear Operators: General theory |
From inside the book
Results 1-3 of 87
Page 28
... exists a do e D , such that g ( f ( p ) , f ( q ) ) < ɛ if p≥ do , q≥ do . 5 LEMMA . If f is a generalized Cauchy sequence in a complete metric space X , there exists a pe X such that lim f ( d ) .. p . PROOF . Let de D be such that ...
... exists a do e D , such that g ( f ( p ) , f ( q ) ) < ɛ if p≥ do , q≥ do . 5 LEMMA . If f is a generalized Cauchy sequence in a complete metric space X , there exists a pe X such that lim f ( d ) .. p . PROOF . Let de D be such that ...
Page 362
... exists a complex - valued regular measure u in C * with an ∞ = Son ( y ) μ ( dy ) if and only if Σx__ x λmnaμ¤n ( x ) \ dx < K , for all m ≥ 1. Show that there exists an f in L , with a , = f ( y ) f ( y ) dy if and only if in ...
... exists a complex - valued regular measure u in C * with an ∞ = Son ( y ) μ ( dy ) if and only if Σx__ x λmnaμ¤n ( x ) \ dx < K , for all m ≥ 1. Show that there exists an f in L , with a , = f ( y ) f ( y ) dy if and only if in ...
Page 683
... exists for m - almost all points in S. ( It should be noted that the only way in which the requirement that ƒ be bounded is used , is to insure the m - integrability of f . In other words the following proof shows the existence of the ...
... exists for m - almost all points in S. ( It should be noted that the only way in which the requirement that ƒ be bounded is used , is to insure the m - integrability of f . In other words the following proof shows the existence of the ...
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