Linear Operators: General theory |
From inside the book
Results 1-3 of 88
Page 34
... called multiplication . The element ab is called the product of a and b . The product ab is required to satisfy the following conditions : ( i ) a ( bc ) = ( ab ) c , a , b , c e G ; ( ii ) there is an element e in G , called the ...
... called multiplication . The element ab is called the product of a and b . The product ab is required to satisfy the following conditions : ( i ) a ( bc ) = ( ab ) c , a , b , c e G ; ( ii ) there is an element e in G , called the ...
Page 35
... called a homo- morphism if h ( ab ) = h ( a ) h ( b ) . A one - to - one homomorphism is called an isomorphism . If h : A → B is an isomorphism and if h ( A ) = B , then A and B are said to be isomorphic , or A is said to be isomorphic ...
... called a homo- morphism if h ( ab ) = h ( a ) h ( b ) . A one - to - one homomorphism is called an isomorphism . If h : A → B is an isomorphism and if h ( A ) = B , then A and B are said to be isomorphic , or A is said to be isomorphic ...
Page 38
... called the natural homomorphism of X onto M. It is a linear transformation . Unless otherwise stated , the coefficient field Ø for a linear space X will be either the field of real numbers , in which case X is called a real linear space ...
... called the natural homomorphism of X onto M. It is a linear transformation . Unless otherwise stated , the coefficient field Ø for a linear space X will be either the field of real numbers , in which case X is called a real linear space ...
Contents
Exercises | 9 |
Definitions and Basic Properties | 13 |
Metric Spaces | 19 |
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 B₁ ba(S Banach spaces Borel sets Cauchy sequence closed sets compact Hausdorff space compact operator complex numbers contains continuous functions continuous linear converges convex set Corollary countably additive DEFINITION denote dense disjoint Doklady Akad E₁ elements ergodic exists f₁ finite number follows function defined function f Hausdorff space Hence Hilbert space homomorphism integral L₁ L₁(S Lebesgue Lemma Let f linear functional linear map linear operator linear topological space measurable functions measure space metric space Nauk SSSR N. S. neighborhood non-negative normed linear space open set operator topology positive measure space Proc PROOF properties proved real numbers reflexive Riesz Russian S₁ scalar semi-group sequentially compact Show subset subspace Suppose Theorem theory topological space u-integrable u-measurable u-null uniformly unit sphere vector space weakly compact zero ΕΕΣ