شماره ركورد كنفرانس :
4338
عنوان مقاله :
Domination problem for orthogonally additive operators in vector lattices
پديدآورندگان :
Pliev Marat maratpliev@gmail.com Department of Functional Analysis, Southern Mathematical Institute of the Russian Academy of Sciences,
str. Markusa 22,Vladikavkaz, 362027 Russia and
RUDN University
6 Miklukho-Maklaya st, Moscow;
كليدواژه :
Orthogonally additive operators , $AM$ , compact operators , vector lattices , domination problem
عنوان كنفرانس :
سومين سمينار ملي نظريه عملگرها و كاربردهاي آن
چكيده فارسي :
The ``Up-and-down theorem which describes the structure of the Boolean algebra of fragments of a linear positive operator is the well known result in operator theory. An analog of this theorem for a positive abstract Uryson operator defined on a vector lattice and taking values in a Dedekind complete vector lattice was proven. This result is used to prove a theorem of domination for $AM$-compact positive abstract Uryson operators from a Dedekind complete vector lattice $E$ to a Banach lattice $F$ with an order continuous norm.
