Please use this identifier to cite or link to this item:
|Title:||IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY IN MATHEMATICS|
|Authors:||MARABEH IN, MOHAMMAD A. A.|
|Publisher:||MIDDLE EAST TECHNICAL UNIVERSITY|
|Citation:||MIDDLE EAST TECHNICAL UNIVERSITY|
|Abstract:||The main aim of this thesis is to generalize unbounded order convergence, unbounded norm convergence and unbounded absolute weak convergence to lattice-normed vector lattices (LNVLs). Therefore, we introduce the follwing notion: a net (x ) in an LNVL (X; p;E) is said to be unbounded p-convergent to x 2 X (shortly, x upconverges to x) if p(jx xj ^ u) o ! 0 in E for all u 2 X+. Throughout this thesis, we study general properties of up-convergence. Besides, we introduce several notions in lattice-normed vector lattices which correspond to notions from vector and Banach lattice theory. Finally, we study briefly the mixed-normed spaces and use them for an investigation of up-null nets and up-null sequences in lattice-normed vector lattices. Keywords: Vector Lattice, Lattice-Normed Vector Lattice, up-Convergence, uo-Convergence, un-Convergence, uaw-Convergence, Mixed-Normed Space|
|Appears in Collections:||PH.D|
Files in This Item:
There are no files associated with this item.
Items in DSpace are protected by copyright, with all rights reserved, unless otherwise indicated.