Linear Operators: General theory |
From inside the book
Results 1-3 of 32
Page 91
... homeomorphic to a normed linear space if and only if there exists a bounded convex neighborhood of the origin ... homeomorphism between each of the spaces L , lp , p ≥ 1 , c , co , C [ 0 , 1 ] and the direct sum of these spaces ...
... homeomorphic to a normed linear space if and only if there exists a bounded convex neighborhood of the origin ... homeomorphism between each of the spaces L , lp , p ≥ 1 , c , co , C [ 0 , 1 ] and the direct sum of these spaces ...
Page 157
... homeomorphism of Σ ( u ) onto a subset of M ( S , 2 , μ ) . It is clear that this homeomorphism maps Cauchy sequences into Cauchy sequences . Thus if o ( En , Em ) 0 , there is , by Corollary 6.5 , a function 7 in M ( S , E , μ ) with ...
... homeomorphism of Σ ( u ) onto a subset of M ( S , 2 , μ ) . It is clear that this homeomorphism maps Cauchy sequences into Cauchy sequences . Thus if o ( En , Em ) 0 , there is , by Corollary 6.5 , a function 7 in M ( S , E , μ ) with ...
Page 442
... homeomorphism . Q.E.D. ૨ = x 8 THEOREM . ( Banach - Stone ) Let Q and R be compact Hausdorff spaces , and let T be an isometric isomorphism between C ( Q ) and C ( R ) . Then there exists a homeomorphism τ between R and Q , and a ...
... homeomorphism . Q.E.D. ૨ = x 8 THEOREM . ( Banach - Stone ) Let Q and R be compact Hausdorff spaces , and let T be an isometric isomorphism between C ( Q ) and C ( R ) . Then there exists a homeomorphism τ between R and Q , and a ...
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