A note on b-weakly compact operators

Alpay, Safak
Altin, Birol
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.


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.
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 divisor class groups of degree zero of algebraic function fields over finite fields
Özbudak, Ferruh (Elsevier BV, 2003-01-01)
We give tight upper bounds on the number of degree one places of an algebraic function field over a finite field in terms of the exponent of a natural subgroup of the divisor class group of degree zero.. (C) 2002 Elsevier Science (USA). All rights reserved.
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.
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.
Citation Formats
S. Alpay and B. Altin, “A note on b-weakly compact operators,” POSITIVITY, pp. 575–582, 2007, Accessed: 00, 2020. [Online]. Available: https://hdl.handle.net/11511/65075.