On property (b) of vector lattices

Date

2003-06-01

Author

Alpay, S
Altin, B
Tonyali, C

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A boundedness property is introduced and characterizations of this property are given.

Subject Keywords

Theoretical Computer Science, Analysis, General Mathematics

URI

https://hdl.handle.net/11511/66212

Journal

POSITIVITY

DOI

https://doi.org/10.1023/a:1025840528211

Collections

Department of Mathematics, Article

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On ideals generated by positive operators Alpay, S; Uyar, A (Springer Science and Business Media LLC, 2003-06-01) Algebra structure of principle ideals of order bounded operators is studied.
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.
Invariant subspaces of collectively compact sets of linear operators Alpay, Safak; Misirlioglu, Tunc (Springer Science and Business Media LLC, 2008-01-01) In this paper, we first give some invariant subspace results for collectively compact sets of operators in connection with the joint spectral radius of these sets. We then prove that any collectively compact set M in alg Gamma satisfies Berger-Wang formula, where Gamma is a complete chain of subspaces of X.
Invariant subspaces for positive operators acting on a Banach space with Markushevich basis 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 note on Riesz spaces with property-b Alpay, S.; Altin, B.; Tonyali, C. (Institute of Mathematics, Czech Academy of Sciences, 2006-01-01) We study an order boundedness property in Riesz spaces and investigate Riesz spaces and Banach lattices enjoying this property.

Citation Formats

S. Alpay, B. Altin, and C. Tonyali, “On property (b) of vector lattices,” POSITIVITY, pp. 135–139, 2003, Accessed: 00, 2020. [Online]. Available: https://hdl.handle.net/11511/66212.