Open AccessUnbounded order-norm continuous and unbounded norm continuous operator
Author(s) -
Kazem Haghnejad Azar,
Mina Matin,
Razi Alavizadeh
Publication year - 2021
Publication title -
filomat
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.449
H-Index - 34
eISSN - 2406-0933
pISSN - 0354-5180
DOI - 10.2298/fil2113417a
Subject(s) - mathematics , operator norm , bounded operator , norm (philosophy) , bounded function , dual norm , compact operator , banach space , pure mathematics , operator (biology) , discrete mathematics , finite rank operator , mathematical analysis , repressor , political science , law , computer science , transcription factor , gene , programming language , extension (predicate logic) , biochemistry , chemistry
A continuous operator T between two normed vector lattices E and F is called unbounded order-norm continuous whenever x? uo? 0 implies ||Tx?|| ? 0, for each norm bounded net (x?)? ? E. Let E and F be two Banach lattices. A continuous operator T : E ? F is called unbounded norm continuous, if for each norm bounded net (x?)? ? E, x? un? 0 implies Tx? un? 0. In this manuscript, we study some properties of these classes of operators and investigate their relationships with the other classes of operators.