u tau-convergence in locally solid vector lattices

Dabboorasad, Y. A.
Emelyanov, Eduard
Marabeh, M. A. A.
Let be a net in a locally solid vector lattice ; we say that is unbounded -convergent to a vector if for all . In this paper, we study general properties of unbounded -convergence (shortly -convergence). -convergence generalizes unbounded norm convergence and unbounded absolute weak convergence in normed lattices that have been investigated recently. We introduce -topology and briefly study metrizability and completeness of this topology.


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Ercan, Z; Onal, S (Springer Science and Business Media LLC, 2004-06-01)
We introduce 'weak quasinilpotence' for operators. Then, by substituting 'Markushevich basis' and 'weak quasinilpotence at a nonzero vector' for 'Schauder basis' and 'quasinilpotence at a nonzero vector', respectively, we answer a question on the invariant subspaces of positive operators in [ 3].
A positive doubly power bounded operator with a nonpositive inverse exists on any infinite-dimensional AL-Space
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A note on b-weakly compact operators
Alpay, Safak; Altin, Birol (Springer Science and Business Media LLC, 2007-11-01)
We consider a continuous operator T : E -> X where E is a Banach lattice and X is a Banach space. We characterize the b-weak compactness of T in terms of its mapping properties.
Unbounded asymptotic equivalences of operator nets with applications
ERKURŞUN ÖZCAN, NAZİFE; Gezer, Niyazi Anıl (Springer Science and Business Media LLC, 2019-09-01)
Present paper deals with applications of asymptotic equivalence relations on operator nets. These relations are defined via unbounded convergences on vector lattices. Given two convergences c and delta on a vector lattice, we study delta-asymptotic properties of operator nets formed by c-continuous operators. Asymptotic equivalences are known to be useful and extremely important tools to study infinite behaviors of strongly convergent operator nets and continuous semigroups. After giving a general theory, p...
Characterizations of Riesz spaces with b-property
Alpay, Safak; ERCAN, ZAFER (Springer Science and Business Media LLC, 2009-02-01)
A Riesz space E is said to have b-property if each subset which is order bounded in E(similar to similar to) is order bounded in E. The relationship between b-property and completeness, being a retract and the absolute weak topology vertical bar sigma vertical bar (E(similar to), E) is studied. Perfect Riesz spaces are characterized in terms of b-property. It is shown that b-property coincides with the Levi property in Dedekind complete Frechet lattices.
Citation Formats
Y. A. Dabboorasad, E. Emelyanov, and M. A. A. Marabeh, “u tau-convergence in locally solid vector lattices,” POSITIVITY, pp. 1065–1080, 2018, Accessed: 00, 2020. [Online]. Available: https://hdl.handle.net/11511/41488.