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Open AccessDuals of Cesàro sequence vector lattices, Cesàro sums of Banach lattices, and their finite elements
In this paper, we study the ideals of finite elements in special vector lattices of real sequences, first in the duals of Cesàro sequence spaces ...
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Article
FINITE ELEMENTS IN ORDERED BANACH SPACES WITH POSITIVE BASES
We characterize finite elements, an order-theoretic concept in Archimedean vector lattices, in the setting of ordered Banach spaces with positive unconditional basis as vectors having finite support with respe...
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Article
Cesàro vector lattices and their ideals of finite elements
For the Cesàro matrix \(C=(c_{nm})_{n,m\in \mathbb {N}}\) C = ...
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Article
On self-majorizing elements in Archimedean vector lattices
A finite element in an Archimedean vector lattice is called self-majorizing if its modulus is a majorant. Such elements exist in many vector lattices and naturally occur in different contexts. They are also kn...
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Article
On finite elements in \(f\) -algebras and in product algebras
Finite elements, which are well-known and studied in the framework of vector lattices, are investigated in \(\ell \) -...
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Article
On some vector lattices of operators and their finite elements
If the vector space \({\mathcal{L}}^r(E, F)\) of all regular operators between the vector lattices E and F is ordered...
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Article
On Finite Elements in Lattices of Regular Operators
Let E and F be vector lattices and \({\mathcal L}^r(E,F)\) the ordered space of all regular operators, which turns ou...