Linear Operators: General theory |
From inside the book
Results 1-3 of 79
Page 204
... zero and since 0 ≤fn ( 8 ) ≤ 1 it follows from the dominated convergence theorem ( 6.16 ) that there is a point in S for which fn ( s ) is defined for all n and for which the se- quence { fn ( s ) } does not converge to zero . Thus ...
... zero and since 0 ≤fn ( 8 ) ≤ 1 it follows from the dominated convergence theorem ( 6.16 ) that there is a point in S for which fn ( s ) is defined for all n and for which the se- quence { fn ( s ) } does not converge to zero . Thus ...
Page 452
... zero continuous linear functional tangent to A at p if and only if the cone B with vertex p generated by A is not ... zero continuous linear functional tangent to B at p is a tangent to A at p . Conversely , if ƒ is a non - zero ...
... zero continuous linear functional tangent to A at p if and only if the cone B with vertex p generated by A is not ... zero continuous linear functional tangent to B at p is a tangent to A at p . Conversely , if ƒ is a non - zero ...
Page 595
... zero in the weak operator topology . Suppose that { fn ( T ) x } is weakly se- quentially compact for each x in X ... zero a in X2 , the sequence { fn ( T ) x } converges to a non - zero element of X. Since f ( T ) commutes with R ( 2 ...
... zero in the weak operator topology . Suppose that { fn ( T ) x } is weakly se- quentially compact for each x in X ... zero a in X2 , the sequence { fn ( T ) x } converges to a non - zero element of X. Since f ( T ) commutes with R ( 2 ...
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