Linear Operators: General theory |
From inside the book
Results 1-3 of 47
Page 119
... consider a function ƒ ( vector or extended real - valued ) which is defined only on the complement of a u - null set ... considering this somewhat more extended class of functions we make no change in F ( S , E , μ , X ) , or in any of ...
... consider a function ƒ ( vector or extended real - valued ) which is defined only on the complement of a u - null set ... considering this somewhat more extended class of functions we make no change in F ( S , E , μ , X ) , or in any of ...
Page 311
... Consider the closed subspace B ( S , E ) of B ( S ) . According to Theorems 6.18 and 6.20 there is a compact Hausdorff space S1 such that B ( S , E ) is equivalent to C ( S1 ) . Theorem 5.1 shows that there is an isometric isomorphism x ...
... Consider the closed subspace B ( S , E ) of B ( S ) . According to Theorems 6.18 and 6.20 there is a compact Hausdorff space S1 such that B ( S , E ) is equivalent to C ( S1 ) . Theorem 5.1 shows that there is an isometric isomorphism x ...
Page 421
... Consider the linear map T : X → E " , defined by T ( x ) = [ f ( x ) , ... , fn ( x ) ] . On the linear subspace T ( X ) of E " , define the mapping y by - y [ T ( x ) ] = y [ f1 ( x ) , = f ( x ) , ... , fn ( x ) ] = · g ( x ) . The ...
... Consider the linear map T : X → E " , defined by T ( x ) = [ f ( x ) , ... , fn ( x ) ] . On the linear subspace T ( X ) of E " , define the mapping y by - y [ T ( x ) ] = y [ f1 ( x ) , = f ( x ) , ... , fn ( x ) ] = · g ( x ) . The ...
Contents
A Settheoretic Preliminaries | 1 |
B Topological Preliminaries | 10 |
Algebraic Preliminaries | 34 |
Copyright | |
59 other sections not shown
Other editions - View all
Common terms and phrases
A₁ Acad additive set function algebra Amer analytic arbitrary B-space 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 exists f₁ finite dimensional function defined function f g₁ 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-measurable uniformly weak topology weakly compact weakly sequentially compact zero ΕΕΣ