caa a22 4500 467932085 CHVBK 20180406152946.0 cr unu---uuuuu 170328e20060101xx s 000 0 eng 10.1007/s00020-004-1335-3 doi (NATIONALLICENCE)springer-10.1007/s00020-004-1335-3 Algebraic Order Bounded Disjointness Preserving Operators and Strongly Diagonal Operators [Elektronische Daten] [Karim Boulabiar, Gerard Buskes, Gleb Sirotkin] Abstract.: Let T be an order bounded disjointness preserving operator on an Archimedean vector lattice. The main result in this paper shows that T is algebraic if and only if there exist natural numbers m and n such that n≥m, and T n!, when restricted to the vector sublattice generated by the range of T m , is an algebraic orthomorphism. Moreover, n (respectively, m) can be chosen as the degree (respectively, the multiplicity of 0 as a root) of the minimal polynomial of T. In the process of proving this result, we define strongly diagonal operators and study algebraic order bounded disjointness preserving operators and locally algebraic orthomorphisms. In addition, we introduce a type of completeness on Archimedean vector lattices that is necessary and sufficient for locally algebraic orthomorphisms to coincide with algebraic orthomorphisms. Birkhäuser Verlag, Basel, 2006 Algebraic operator nationallicence disjointness preserving operator nationallicence minimal polynomial nationallicence orthomorphism nationallicence strongly diagonal operator nationallicence vector lattice nationallicence Boulabiar Karim Institut Préparatoire aux Etudes Scientifiques et Techniques, Univeristé de Carthage, BP 51, 2070, La Marsa, Tunisia aut Buskes Gerard Department of Mathematics, University of Mississippi, 38677, University, MS, USA aut Sirotkin Gleb Department of Mathematics, University of Mississippi, 38677, University, MS, USA aut Integral Equations and Operator Theory Birkhäuser-Verlag; www.birkhauser.ch 54/1(2006-01-01), 9-31 0378-620X 54:1<9 2006 54 20 https://doi.org/10.1007/s00020-004-1335-3 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s00020-004-1335-3 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Boulabiar Karim Institut Préparatoire aux Etudes Scientifiques et Techniques, Univeristé de Carthage, BP 51, 2070, La Marsa, Tunisia aut NATIONALLICENCE 700 1- Buskes Gerard Department of Mathematics, University of Mississippi, 38677, University, MS, USA aut NATIONALLICENCE 700 1- Sirotkin Gleb Department of Mathematics, University of Mississippi, 38677, University, MS, USA aut NATIONALLICENCE 773 0- Integral Equations and Operator Theory Birkhäuser-Verlag; www.birkhauser.ch 54/1(2006-01-01), 9-31 0378-620X 54:1<9 2006 54 20 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer