Linear Operators: General theory |
From inside the book
Results 1-3 of 60
Page 12
... closure of A in this topology . PROOF . Statements 10 ( b ) , ( d ) show that o , Xe F , and 10 ( a ) shows that A Be F if A , Be F. It follows that any finite union of sets in F is in F. From 10 ( a ) , it follows that AC B implies ĀC ...
... closure of A in this topology . PROOF . Statements 10 ( b ) , ( d ) show that o , Xe F , and 10 ( a ) shows that A Be F if A , Be F. It follows that any finite union of sets in F is in F. From 10 ( a ) , it follows that AC B implies ĀC ...
Page 432
... closure of x ( A ) , there is an element zm € A such that = \ x * ( m ) —x ** ( x * ) | < 1 / m , i = 1 , n . Since A is weakly sequentially compact , a subsequence of { m } will converge weakly to an element z which is certainly in A ...
... closure of x ( A ) , there is an element zm € A such that = \ x * ( m ) —x ** ( x * ) | < 1 / m , i = 1 , n . Since A is weakly sequentially compact , a subsequence of { m } will converge weakly to an element z which is certainly in A ...
Page 511
... closure of co ( A ) . If A is compact in the strong operator topology , so is the strong operator closure of co ( 4 ) . 4 If a set AC B ( X , Y ) is sequentially compact in the weak operator topology , its weak operator closure is ...
... closure of co ( A ) . If A is compact in the strong operator topology , so is the strong operator closure of co ( 4 ) . 4 If a set AC B ( X , Y ) is sequentially compact in the weak operator topology , its weak operator closure is ...
Contents
Preliminary Concepts | 1 |
B Topological Preliminaries | 10 |
Algebraic Preliminaries | 34 |
Copyright | |
80 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 ca(S Cauchy sequence compact Hausdorff space compact operator complex numbers contains continuous functions converges convex set Corollary countably additive DEFINITION dense disjoint Doklady Akad E₁ element ergodic exists f₁ finite dimensional function defined function f Hausdorff space Hence Hilbert space homeomorphism implies inequality integral isometric isomorphism K₁ L₁ L₁(S Lebesgue Lemma Let f linear manifold linear map linear operator linear topological space measurable functions measure space metric space Nauk SSSR N. S. neighborhood non-negative o-field o-finite open set operator topology positive measure space Proc PROOF properties proved real numbers reflexive Riesz S₁ scalar semi-group sequentially compact Show subset subspace Suppose theory topological space u-integrable u-measurable uniformly weak topology weakly compact weakly sequentially compact zero ΕΕΣ