On Banach lattices with Levi norms
Birol Altın
- Vol. 135, Iss: 4, pp 1059-1063
TLDR
In this paper, the authors generalized Schmidt's result to Banach lattices with Levi-Fatou norm serving as range, and some characterizations of Riesz spaces having property (b) are also obtained.Abstract:
Schmidt proved that an operator T from a Banach lattice E into a Banach lattice G with property (P) is order bounded if and only if its adjoint is order bounded, and in this case T satisfies |||T||| = |||T'|||. In the present paper the result is generalized to Banach lattices with Levi-Fatou norm serving as range, and some characterizations of Banach lattices with a Levi norm are given. Moreover, some characterizations of Riesz spaces having property (b) are also obtained.read more
Citations
More filters
Journal ArticleDOI
A Note on b-Weakly Compact Operators
Şafak Alpay,Birol Altın +1 more
TL;DR: In this article, the b-weak compactness of a continuous operator T: E → X where X is a Banach space and E is a lattice, is characterized in terms of its mapping properties.
Journal ArticleDOI
Characterizations of Riesz spaces with b-property
Şafak Alpay,Zafer Ercan +1 more
TL;DR: In this paper, the relationship between b-property and completeness, being a retract and the absolute weak topology |σ|(E~, E) is studied, and the Levi property coincides with the Dedekind complete Frechet lattices.
ON RIESZ SPACES WITH b-PROPERTY AND b-WEAKLY COMPACT OPERATORS
Alpay Safak,Altin Birol +1 more
TL;DR: In this article, the authors characterize b-weakly compact operators among o-weak-compact operators and discuss relation between Dunford-Pettis operators and b-Weakly Compact operators.
Journal Article
On Operators of Strong Type B
TL;DR: In this paper, the authors discuss operators of strong type B between a Banach lattice and a space and give necessary and sufficient conditions for this class of operators to coincide with weakly compact operators.
Journal ArticleDOI
On Riesz spaces with b -property and strongly order bounded operators
Şafak Alpay,Birol Altın +1 more
TL;DR: In this paper, the relationship between the b-property and various classes of operators is studied in Riesz spaces with bidual order-bounded subsets, where each subset that is order bounded in the bidual remains to be ordered in E.
References
More filters
Book
Positive Operators
TL;DR: Book of positive operators, as an amazing reference becomes what you need to get, and book, as a source that may involve the facts, opinion, literature, religion, and many others are the great friends to join with.
Journal ArticleDOI
On Property (b) of Vector Lattices
TL;DR: In this article, a boundedness property is introduced and characterizations of this property are given, where the boundedness is defined as the property that a property is bounded by a set of properties.
Journal ArticleDOI
When each continuous operator is regular, II
TL;DR: In this article, it was shown that the Levi condition is necessary for the validity of equality in a Banach lattice with the Levi norm, but not for a Dedekind complete Banach.
Journal ArticleDOI
A note on Riesz spaces with property-b
TL;DR: In this paper, an order boundedness property in Riesz spaces and Banach lattices was studied. But this property was not studied in the context of order bounded spaces.