Geodesic
Unbounded order-norm continuous and unbounded norm continuous operator
Filomat, Tome 35 (2021) no. 13, p. 4417

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DOI

A continuous operator T between two normed vector lattices E and F is called unbounded order-norm continuous whenever x α uo − → 0 implies Tx α → 0, for each norm bounded net (x α) α ⊆ 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 α) α ⊆ E, x α un − → 0 implies Tx α un − → 0. In this manuscript, we study some properties of these classes of operators and investigate their relationships with the other classes of operators
DOI : 10.2298/FIL2113417A
Classification : 47B60, 46A40
Keywords: unboundedσ-order-norm continuous, unbounded order-norm continuous, σ-unbounded norm continuous, unbounded norm continuous, un-compact 
Kazem Haghnejad Azar; Mina Matin; Razi Alavizadeh. Unbounded order-norm continuous and unbounded norm continuous operator. Filomat, Tome 35 (2021) no. 13, p. 4417 . doi: 10.2298/FIL2113417A
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     title = {Unbounded order-norm continuous and unbounded norm continuous operator},
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     pages = {4417 },
     year = {2021},
     volume = {35},
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     doi = {10.2298/FIL2113417A},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.2298/FIL2113417A/}
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