Linear Operators: General theory |
From inside the book
Results 1-3 of 91
Page 36
... linear vector space , linear space , or vector space over a field 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 ...
... linear vector space , linear space , or vector space over a field 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 ...
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 : 3 are linear transformations ...
... 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 : 3 are linear transformations ...
Page 49
... linear vector spaces will be over the field of real or the field of complex numbers . A real vector space is one for which the field is the set of real numbers ; a complex vector space is one for which is the set of complex numbers ...
... linear vector spaces will be over the field of real or the field of complex numbers . A real vector space is one for which the field is the set of real numbers ; a complex vector space is one for which is the set of complex numbers ...
Contents
A Settheoretic Preliminaries | 1 |
10 | 30 |
Three Basic Principles of Linear Analysis | 49 |
Copyright | |
31 other sections not shown
Other editions - View all
Common terms and phrases
A₁ additive set function algebra analytic arbitrary B-space B₁ ba(S Banach Borel sets ca(S Cauchy sequence closed unit sphere compact Hausdorff space compact operator complex numbers conditionally compact contains continuous functions convex set Corollary countably additive DEFINITION denote dense E₁ element equation equivalent exists f₁ finite dimensional function defined function f Hausdorff space Hence Hilbert space homeomorphism implies inequality integral isometric isomorphism K₁ L₁ L₁(S Lebesgue measure Lemma Let f linear map linear operator linear topological space Math measurable functions measure space metric space neighborhood non-negative non-zero normed linear space o-field o-finite open set operator topology positive measure space properties proved real numbers reflexive Riesz S₁ scalar semi-group sequentially compact Show subset subspace Suppose theory TM(S topological space u-integrable u-measurable uniformly valued function weak topology weakly compact weakly sequentially compact X₁ zero ΕΕΣ