Linear Operators: General theory |
From inside the book
Results 1-3 of 88
Page 36
... vector space , linear space , or vector space over a field Ø is an additive group together with an operation m : xX → X , written as m ( x , x ) = xx , which satisfy the following four conditions : ( i ) a ( x + y ) = ax + ay , αεΦ , α ...
... vector space , linear space , or vector space over a field Ø is an additive group together with an operation m : xX → X , written as m ( x , x ) = xx , which satisfy the following four conditions : ( i ) a ( x + y ) = ax + ay , αεΦ , α ...
Page 37
... vectors in the domain of T. Thus a linear transformation on a linear space X is a homomorphism on the additive group X which commutes with the operations of multiplication by scalars . If T : X → Y and U : Y → 3 are linear ...
... vectors in the domain of T. Thus a linear transformation on a linear space X is a homomorphism on the additive group X which commutes with the operations of multiplication by scalars . If T : X → Y and U : Y → 3 are linear ...
Page 58
... linear space is an F - space under each of two metrics , and if one of the corresponding topologies contains the other , the two topologies are equal . = PROOF . Let T1 , T2 be metric topologies in the linear space for which the spaces ...
... linear space is an F - space under each of two metrics , and if one of the corresponding topologies contains the other , the two topologies are equal . = PROOF . Let T1 , T2 be metric topologies in the linear space for which the spaces ...
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