Linear Operators: General theory |
From inside the book
Results 1-3 of 82
Page 188
... corollary is the o - finite analogue of Corollary 4 . 7 COROLLARY . Let ( S , E , u ) be the product of two positive o - finite measure spaces ( S1 , E1 , μ1 ) and ( S2 , Z2 , 2 ) . For each E in Σ and są in S , the set E ( 82 ) = { 81 ...
... corollary is the o - finite analogue of Corollary 4 . 7 COROLLARY . Let ( S , E , u ) be the product of two positive o - finite measure spaces ( S1 , E1 , μ1 ) and ( S2 , Z2 , 2 ) . For each E in Σ and są in S , the set E ( 82 ) = { 81 ...
Page 246
... corollary was established during the first part of the preceding proof . 7 COROLLARY . If { b1 , ... , bn } is a Hamel basis for the normed linear space X then the functionals b * , i = 1 , . . . , n , defined by the equa- tions n x = Σ ...
... corollary was established during the first part of the preceding proof . 7 COROLLARY . If { b1 , ... , bn } is a Hamel basis for the normed linear space X then the functionals b * , i = 1 , . . . , n , defined by the equa- tions n x = Σ ...
Page 422
... Corollary 2.12 , there is a T - continuous fo and a constant c such that RfoY ) ≤ c , fo ( x ) ‡ 0 . By Lemma 1.11 , ƒ 。( Y ) 0 ; by Theorem 9 , foe T. Put f = folfo ( x ) , and the corollary is proved . Q.E.D. 13 THEOREM . A convex ...
... Corollary 2.12 , there is a T - continuous fo and a constant c such that RfoY ) ≤ c , fo ( x ) ‡ 0 . By Lemma 1.11 , ƒ 。( Y ) 0 ; by Theorem 9 , foe T. Put f = folfo ( x ) , and the corollary is proved . Q.E.D. 13 THEOREM . A convex ...
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