Linear Operators: General theory |
From inside the book
Results 1-3 of 91
Page 177
Nelson Dunford, Jacob T. Schwartz. may be assumed that λ is real valued . A real valued set function can be represented as the difference of its positive and negative variations ( 4.11 ) and so we may also assume that λ is positive . Let ...
Nelson Dunford, Jacob T. Schwartz. may be assumed that λ is real valued . A real valued set function can be represented as the difference of its positive and negative variations ( 4.11 ) and so we may also assume that λ is positive . Let ...
Page 178
... assume that v ( u , F ) < ∞ and v ( 2 , F ) < ∞ . Since g is λ - measurable there is a sequence { g } of simple functions converging to g ( s ) for every s in F except on a set ECF with v ( 2 , E ) = 0 ( by Corollary 6.13 ( a ) ...
... assume that v ( u , F ) < ∞ and v ( 2 , F ) < ∞ . Since g is λ - measurable there is a sequence { g } of simple functions converging to g ( s ) for every s in F except on a set ECF with v ( 2 , E ) = 0 ( by Corollary 6.13 ( a ) ...
Page 535
... Assume μ ( S ) = ≤ 1. Put exp { √ ̧ log | f ( s ) \ μ ( ds ) } = \ f \。 for f in Lo ( S , E , μ ) . Show that if ƒ and g are non - negative functions in L。( S , E , μ ) , then [ ƒ + g│。≥ fo + go . ( Hint . Use Exercise III.9.29 ...
... Assume μ ( S ) = ≤ 1. Put exp { √ ̧ log | f ( s ) \ μ ( ds ) } = \ f \。 for f in Lo ( S , E , μ ) . Show that if ƒ and g are non - negative functions in L。( S , E , μ ) , then [ ƒ + g│。≥ fo + go . ( Hint . Use Exercise III.9.29 ...
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