scholarly journals On band preserving orthogonally additive operators

2021 ◽  
Vol 18 (1) ◽  
pp. 495-510
Author(s):  
N. M. Abasov
Keyword(s):  
Orthogonally Additive ◽  
Orthogonally Additive Operators

scholarly journals Narrow orthogonally additive operators

Positivity ◽  
2013 ◽  
Vol 18 (4) ◽  
pp. 641-667 ◽  
Author(s):  
Marat Pliev ◽  
Mikhail Popov
Keyword(s):  
Orthogonally Additive ◽  
Orthogonally Additive Operators

scholarly journals ON SEPARATE ORDER CONTINUITY OF ORTHOGONALLY ADDITIVE OPERATORS

2021 ◽  
Vol 9 (1) ◽  
pp. 200-209
Author(s):  
I. Krasikova ◽  
O. Fotiy ◽  
M. Pliev ◽  
M. Popov
Keyword(s):  
Order Continuity ◽  
Vector Lattices ◽  
Additive Operator ◽  
Uniformly Convergent ◽  
Orthogonally Additive Operator ◽  
Orthogonally Additive ◽  
Order Continuous ◽  
Orthogonally Additive Operators

Our main result asserts that, under some assumptions, the uniformly-to-order continuity of an order bounded orthogonally additive operator between vector lattices together with its horizontally-to-order continuity implies its order continuity (we say that a mapping f : E → F between vector lattices E and F is horizontally-to-order continuous provided f sends laterally increasing order convergent nets in E to order convergent nets in F, and f is uniformly-to-order continuous provided f sends uniformly convergent nets to order convergent nets).

scholarly journals On Sums of Strictly Narrow Operators Acting from a Riesz Space to a Banach Space

2019 ◽  
Vol 2019 ◽  
pp. 1-6
Author(s):  
Oleksandr Maslyuchenko ◽  
Mikhail Popov
Keyword(s):  
Banach Space ◽  
Finite Rank ◽  
Riesz Space ◽  
The Other ◽  
Finite Variation ◽  
Orthogonally Additive ◽  
Orthogonally Additive Operators

We prove that ifEis a Dedekind complete atomless Riesz space andXis a Banach space, then the sum of two laterally continuous orthogonally additive operators fromEtoX, one of which is strictly narrow and the other one is hereditarily strictly narrow with finite variation (in particular, has finite rank), is strictly narrow. Similar results were previously obtained for narrow operators by different authors; however, no theorem of the kind was known for strictly narrow operators.

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