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pro vyhledávání: '"Emelyanov, E. Yu."'
Let $x_\alpha$ be a net in a locally solid vector lattice $(X,\tau)$; we say that $x_\alpha$ is unbounded $\tau$-convergent to a vector $x\in X$ if $\lvert x_\alpha-x \rvert\wedge w \xrightarrow{\tau} 0$ for all $w\in X_+$. In this paper, we study ge
Externí odkaz:
http://arxiv.org/abs/1706.02006
A linear operator $T$ between two lattice-normed spaces is said to be $p$-compact if, for any $p$-bounded net $x_\alpha$, the net $Tx_\alpha$ has a $p$-convergent subnet. $p$-Compact operators generalize several known classes of operators such as com
Externí odkaz:
http://arxiv.org/abs/1701.03073
A net $x_\alpha$ in a lattice-normed vector lattice $(X,p,E)$ is unbounded $p$-convergent to $x\in X$ if $p(|x_\alpha-x|\wedge u)\xrightarrow{o} 0$ for every $u\in X_+$. This convergence has been investigated recently for $(X,p,E)=(X,\lvert\cdot \rve
Externí odkaz:
http://arxiv.org/abs/1609.05301
Autor:
Gorokhova, S. G.1 (AUTHOR) lanagor71@gmail.com, Emelyanov, E. Yu.2 (AUTHOR)
Publikováno v:
Siberian Mathematical Journal. May2023, Vol. 64 Issue 3, p720-724. 5p.
Let be a net in a locally solid vector lattice; we say that is unbounded-convergent to a vector if\(| x_\alpha-x|\wedge w\xrightarrow {\tau} 0\) for all. In this paper, we study general properties of unbounded-convergence (shortly-convergence).-conve
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=od______4294::f9a891067e154e5f416489e0d52c9c01
https://link.springer.com/article/10.1007/s11117-018-0559-4
https://link.springer.com/article/10.1007/s11117-018-0559-4
on the occas'ion of hi,s 65th anniuersary Various convergences in vector lattices were historicalll' a subject of deep investigation v'hich stems from the begining of the 20th century in works of Riesz, Kantorovich, Nakano, !'ulikh, Zanen, a',d marl)
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=od______4294::173ceb1d19b52c61925bee5fef50dc22
https://www.researchgate.net/publication/326224364_Unbounded_Convergence_in_the_Convergence_Vector_Lattices_a_Survey
https://www.researchgate.net/publication/326224364_Unbounded_Convergence_in_the_Convergence_Vector_Lattices_a_Survey
Let be a separating family of lattice seminorms on a vector lattice X, then is called a multi-normed vector lattice (or MNVL). We write if for all . A net in an MNVL is said to be unbounded m-convergent (or um-convergent) to x if for all . um-Converg
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=od______4294::8daf3cc5b04d93ea89a2c70cd0b0d7ab
https://link.springer.com/article/10.1007/s11117-017-0533-6
https://link.springer.com/article/10.1007/s11117-017-0533-6
In this note, we show that the order convergence in a vector lattice is not topological unless . Furthermore, we show that, in atomic order continuous Banach lattices, the order convergence is topological on order intervals. Subjects: Functional Anal
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::853fa55e777075297268c2792f3b189e
http://arxiv.org/abs/1705.09883
http://arxiv.org/abs/1705.09883
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A net $x_\alpha$ in a lattice-normed vector lattice $(X,p,E)$ is unbounded $p$-convergent to $x\in X$ if $p(|x_\alpha-x|\wedge u)\xrightarrow{o} 0$ for every $u\in X_+$. This convergence has been investigated recently for $(X,p,E)=(X,\lvert\cdot \rve
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::0d4d01423bfb61250f21dc439105202e
http://arxiv.org/abs/1609.05301
http://arxiv.org/abs/1609.05301