[Turkmath:934] hacettepe matematik bölüm semineri, 6 ocak çarşamba

[Mesut Şahin]

Hacettepe Üniversitesi Bölüm Seminerleri
Unbounded Order Continuous Operators
Mohammad Marabeh
ODTÜ, Türkiye
Özet : A linear operator between two Riesz spaces E and F is said to be
unbounded order continuous (or uo-continuous, for short) whenever it maps
each unbounded order null net in E into an unbounded order null net in F,
and it said to be-unbounded order continuous (or uo-continuous, for short)
if each unbounded order null sequence in E is mapped into an unbounded
order null sequence in F. We begin this talk by a review of some basic
notions and results from the theory of Riesz spaces. Then we will recall
the unbounded order convergence"(abbreviated, uo-convergence) of nets in
Riesz spaces, and demonstrate some recent characterizations of it. Later we
will give some properties of uo-continuous and uo-continuous operators. We
will also characterize the uo-continuous (respectively, uo-continuous) dual
of some well-known Riesz spaces. Finally, as an application of
uo-convergence and uo-continuity we establish two variants of Brezis-Lieb
lemma in Riesz spaces. PS:This work is a part of ongoing thesis under
supervision of Prof. Eduard Emelyanov, Orta Dogu Teknik Universitesi
(ODTU).
  Tarih : 06.01.2016   Saat : 15:00   Yer : Yaşar Ataman Salonu, Matematik
Bölümü   Dil : İngilizce




  Mesut Sahin
  Associate Professor
  Department of Mathematics
  Hacettepe University
  TR 06800 Beytepe
  ANKARA - TURKEY
 http://yunus.hacettepe.edu.tr/~mesut.sahin
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