o tau-Continuous, Lebesgue, KB, and Levi Operators Between Vector Lattices and Topological Vector Spaces

Download
2022-06-01
Alpay, Safak
Emelyanov, Eduard
Gorokhova, Svetlana
We investigate o tau-continuous/bounded/compact and Lebesgue operators from vector lattices to topological vector spaces; the Kantorovich-Banach operators between locally solid lattices and topological vector spaces; and the Levi operators from locally solid lattices to vector lattices. The main idea of operator versions of notions related to vector lattices lies in redistributing topological and order properties of a topological vector lattice between the domain and range of an operator under investigation. Domination properties for these classes of operators are studied.
RESULTS IN MATHEMATICS

Suggestions

uτ-Convergence in locally solid vector lattices
Dabboorasad, Yousef A M; Emel’yanov, Eduard; Department of Mathematics (2018)
We say that a net (xα) in a locally solid vector lattice (X,τ) is uτ-convergent to a vector x ∈ X if
Bibounded uo-convergence and b-property in vector lattices
Alpay, Safak; Emelyanov, Eduard; Gorokhova, Svetlana (2021-01-01)
We define bidual bounded uo-convergence in vector lattices and investigate relations between this convergence and b-property. We prove that for a regular Riesz dual system ⟨ X, X∼⟩ , X has b-property if and only if the order convergence in X agrees with the order convergence in X∼ ∼.
Some finite-dimensional backward shift-invariant subspaces in the ball and a related factorization problem
Alpay, D; Kaptanoglu, HT (2000-12-15)
Beurling's theorem characterizes subspaces of the Hardy space invariant under the forward-shift operator in terms of inner functions. In this Note we consider the case where the ball replaces the open unit desk and the reproducing kernel Hilbert space with reproducing kernel 1/(1-Sigma (N)(1) a(j)w(j)*) replaces the Hardy space. We give explicit formulas which generalize Blaschke products in the case of spaces of finite codimension. (C) 2000 Academie des sciences/Editions scientifiques et medicales Elsevier...
SPACES OF u tau-DUNFORD-PETTIS AND u tau-COMPACT OPERATORS ON LOCALLY SOLID VECTOR LATTICES
ERKURŞUN ÖZCAN, NAZİFE; Gezer, Niyazi Anıl; Zabeti, Omid (2019-01-01)
Suppose X is a locally solid vector lattice. It is known that there are several non-equivalent spaces of bounded operators on X. In this paper, we consider some situations under which these classes of bounded operators form locally solid vector lattices. In addition, we generalize some notions of uaw-Dunford-Pettis operators and uaw-compact operators defined on a Banach lattice to general theme of locally solid vector lattices. With the aid of appropriate topologies, we investigate some relations between to...
ON OPERATORS OF STRONG TYPE B
Alpay, Safak (2012-10-01)
We discuss operators of strong type B between a Banach lattice and a Banach space and give necessary and sufficient conditions for this class of operators to coincide with weakly compact operators.
Citation Formats
S. Alpay, E. Emelyanov, and S. Gorokhova, “o tau-Continuous, Lebesgue, KB, and Levi Operators Between Vector Lattices and Topological Vector Spaces,” RESULTS IN MATHEMATICS, vol. 77, no. 3, pp. 0–0, 2022, Accessed: 00, 2022. [Online]. Available: https://hdl.handle.net/11511/97292.