Radon–Riesz property: Normed Vector Space, Limit of a Sequence, Operator Norm, Weak Topology, Banach Space, Hilbert Space, Johann Radon, Frigyes Riesz, Functional Analysis - Couverture souple

 
9786130343729: Radon–Riesz property: Normed Vector Space, Limit of a Sequence, Operator Norm, Weak Topology, Banach Space, Hilbert Space, Johann Radon, Frigyes Riesz, Functional Analysis
Couverture souple
ISBN 10 : 6130343728 ISBN 13 : 9786130343729
Editeur : Betascript Publishing, 2010

Synopsis

Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. The Radon–Riesz property is a mathematical property for normed spaces that helps ensure convergence in norm. Essentially, given two assumptions (essentially weak convergence and continuity of norm), we would like to ensure convergence in the norm topology.Suppose that (X, ||·||) is a normed space. We say that X has the Radon–Riesz property (or that X is a Radon–Riesz space) if whenever (xn) is a sequence in the space and x is a member of X such that (xn) converges converges weakly to x and lim_{ntoinfty} Vert x_n Vert = Vert xVert , then (xn) converges to x in norm; that is, lim_{ntoinfty} Vert x_n - xVert = 0 . Although it would appear that Johann Radon was one of the first to make significant use of the this property in 1913, M. I. Kadets and V. L. Klee also used versions of the Radon–Riesz property to make advancements in Banach space theory in the late 1920s. It is common for the Radon–Riesz property to also be referred to as the Kadets–Klee property or property (H). According to Robert Megginson, the letter H does not stand for anything. It was simply referred to as property (H) in a list of properties for normed spaces that starts with (A) and ends with (H).

Les informations fournies dans la section « Synopsis » peuvent faire référence à une autre édition de ce titre.

Présentation de l'éditeur

Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. The Radon–Riesz property is a mathematical property for normed spaces that helps ensure convergence in norm. Essentially, given two assumptions (essentially weak convergence and continuity of norm), we would like to ensure convergence in the norm topology.Suppose that (X, ||·||) is a normed space. We say that X has the Radon–Riesz property (or that X is a Radon–Riesz space) if whenever (xn) is a sequence in the space and x is a member of X such that (xn) converges converges weakly to x and lim_{ntoinfty} Vert x_n Vert = Vert xVert , then (xn) converges to x in norm; that is, lim_{ntoinfty} Vert x_n - xVert = 0 . Although it would appear that Johann Radon was one of the first to make significant use of the this property in 1913, M. I. Kadets and V. L. Klee also used versions of the Radon–Riesz property to make advancements in Banach space theory in the late 1920s. It is common for the Radon–Riesz property to also be referred to as the Kadets–Klee property or property (H). According to Robert Megginson, the letter H does not stand for anything. It was simply referred to as property (H) in a list of properties for normed spaces that starts with (A) and ends with (H).

Les informations fournies dans la section « A propos du livre » peuvent faire référence à une autre édition de ce titre.

Éditeur
Betascript Publishing
Date d'édition
2010
Langue
anglais
ISBN 10 
6130343728
ISBN 13 
9786130343729
Reliure
Broché
Nombre de pages
80
Éditeur
Surhone Lambert M., Tennoe Mariam T., Henssonow Susan F.
Coordonnées du fabricant
non disponible
Personne responsable
non disponible

Autres éditions populaires du même titre

9786130343330: Radon–Riesz property: Normed Vector Space, Limit of a Sequence, Operator Norm, Weak Topology, Johann Radon, Banach Space, Frigyes Riesz, Hilbert Space, Functional Analysis, Schur's Property

Edition présentée

ISBN 10 :  6130343337 ISBN 13 :  9786130343330
Editeur : Betascript Publishing, 2010
Couverture souple