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تحلل الحزم المتجهة البناخية القابلة للانفصال في الحقول اقياسية من الحزم البناخية == The Decomposition of Separable Banach - Vector Lattice into A Measurable Field of Banach Lattice
Author name:
زينب حسن عبود
Supervisor name:
علي حسين بتور
General topic:
Mathematics
Specific topic:
Mathematics
Degree:
Master
University:
University of Kufa - College Of Education For Girls - Department Of Mathematics
Language:
English
University location:
Najaf
First pages:
27T1106 - p.pdf
Abstract:
his study deals with measurable families of - Banach lattices and the decomposition of a separable Banach - vector lattices into a measurable fields of Banach lattices . It is established that any separable Banach - vector lattice permits a decomposition into measurable fields of ordinary Banach lattices .This thesis consists of three chapters : Chapter one is divided into two sections , chapter two is divided into three sections and chapter three is divided into two sections.In chapter one and two some definitions are introduced as well as the theorems and the basic facts that used in our work .Chapter three includes the fundamental results : 1) If ̂ be the set of all classes for P - almost everywhere coinciding elements from a measurable field of Banach spaces , then Archimedean condition is satisfied in ̂ .2) Let be a measurable field of Banach space generating ̂, then , we can define a structure Banach Lattice on such that , the order in for almost everywhere induces the order in ̂ .3) The Freudenthal unit exists in ̂ , if and only if , it exists in almost everywhere .4) Let be a measurable field of Banach lattice , then ( ̂ ‖ ‖ ̂ is a separable Banach ̂ - vector lattice .5) Let ̂ ‖ ‖ ̂ be a separable Banach ̂ - vector lattices and let be a measurable field of Banach space generating ̂ . Then , it is possible to determine a partial order on such that ̂ ‖ ‖ will be a Banach lattice and ̂ ‖ ‖ ̂ will be a measurable field of Banach lattice for P - almost every .
