Invariant subspaces of collectively compact sets of linear operators

Alpay, Safak
Misirlioglu, Tunc
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].
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.
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.
Dosi, Anar (World Scientific Pub Co Pte Lt, 2011-04-01)
In this note we investigate quantizations of the weak topology associated with a pair of dual linear spaces. We prove that the weak topology admits only one quantization called the weak quantum topology, and that weakly matrix bounded sets are precisely the min-bounded sets with respect to any polynormed topology compatible with the given duality. The technique of this paper allows us to obtain an operator space proof of the noncommutative bipolar theorem.
Citation Formats
S. Alpay and T. Misirlioglu, “Invariant subspaces of collectively compact sets of linear operators,” POSITIVITY, pp. 209–219, 2008, Accessed: 00, 2020. [Online]. Available: