Linear Operators: General theory |
From inside the book
Results 1-3 of 77
Page 36
... linear space , or vector space over a field Þ is an additive group together with an operation m : Ø × X → X ... linear combination of the vectors x , y , . . . , z . A linear subspace , subspace or linear manifold in a vector space , is ...
... linear space , or vector space over a field Þ is an additive group together with an operation m : Ø × X → X ... linear combination of the vectors x , y , . . . , z . A linear subspace , subspace or linear manifold in a vector space , is ...
Page 418
... linear topological space X , and if K1 is compact , then some non - zero continuous linear functional on X separates K1 and K. 12 COROLLARY . If K is a closed convex subset of a locally convex linear topological space , and p & K , then ...
... linear topological space X , and if K1 is compact , then some non - zero continuous linear functional on X separates K1 and K. 12 COROLLARY . If K is a closed convex subset of a locally convex linear topological space , and p & K , then ...
Page 421
... linear space , and let l ' be a total subspace of X. Then the linear functionals on X which are continuous in the I topology are precisely the functionals in T. The proof of Theorem 9 will be based on the following lemma . 10 .... LEMMA ...
... linear space , and let l ' be a total subspace of X. Then the linear functionals on X which are continuous in the I topology are precisely the functionals in T. The proof of Theorem 9 will be based on the following lemma . 10 .... LEMMA ...
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