On Riesz spaces with b-property and strongly order bounded operators

2011 ◽  
Vol 60 (1-2) ◽  
pp. 1-12 ◽  
Author(s):  
Şafak Alpay ◽  
Birol Altın
Keyword(s):  
Bounded Operators ◽  
Riesz Spaces

scholarly journals Решеточная структура в пространстве ограниченных гомоморфизмов между топологическими решеточно упорядоченными кольцами

2019 ◽  
Author(s):  
O. Zabeti
Keyword(s):  
Lattice Structure ◽  
Bounded Operators ◽  
Topological Ring ◽  
Topological Structures ◽  
Riesz Spaces ◽  
Topological Lattice ◽  
Bounded Group

Suppose X is a topological ring. It is known that there are three classes of bounded group homomorphisms on X whose topological structures make them again topological rings. First, we show that if X is a Hausdorff topological ring, then so are these classes of bounded group homomorphisms on X. Now, assume that X is a locally solid lattice ring. In this paper, our aim is to consider lattice structure on these classes of bounded group homomorphisms more precisely, we show that, under some mild assumptions, they are locally solid lattice rings. In fact, we consider bounded order bounded homomorphisms on X. Then we show that under the assumed topology, they form locally solid lattice rings. For this reason, we need a version of the remarkable RieszKantorovich formulae for order bounded operators in Riesz spaces in terms of order bounded homomorphisms on topological lattice groups.

Some characterizations of Riesz spaces in the sense of strongly order bounded operators

Positivity ◽  
2019 ◽  
Vol 24 (1) ◽  
pp. 117-127
Author(s):  
Seyed AliReza Jalili ◽  
Mohammad Bagher Farshbaf Moghimi ◽  
Kazem Haghnejad Azar ◽  
Abbas Najati ◽  
Razi Alavizadeh ◽  
...  
Keyword(s):  
Bounded Operators ◽  
Riesz Spaces

scholarly journals A note on the relationship between three classes of operators on Riesz spaces

2019 ◽  
Vol 57 (2) ◽  
pp. 77-85
Author(s):  
Liang Hong
Keyword(s):  
Bounded Operators ◽  
Riesz Spaces ◽  
Prior Literature ◽  
Continuous Operators ◽  
The Relationship

Abstract Following several papers in the prior literature, we study the relationship between order bounded operators, topologically bounded operators and topologically continuous operators. Our main contribution is two-folded: (i) we provide a set of counterexamples to illustrate several extant results in the literature; (ii) we give conditions for the space of order bounded operators to coincide with the space of topologically bounded operators as well as conditions for these two spaces to coincide with the space of topologically continuous operators.

scholarly journals A NOTE ON LATTICE OPERATIONS OF RIESZ SPACES OF ORDER BOUNDED OPERATORS

1990 ◽  
Vol 21 (4) ◽  
pp. 395-398
Author(s):  
BORIS LAVRIČ
Keyword(s):  
Weak Form ◽  
Riesz Space ◽  
Linear Operators ◽  
Spectral Theorem ◽  
Bounded Operators ◽  
Bounded Linear Operators ◽  
Bounded Linear ◽  
Riesz Spaces

Let $L$, $M$ be Archimedean Riesz spaces with $M$ Dedekind complete, and let $\mathcal L_b(L,M )$ be the Riesz space of order bounded linear operators from $L$ into $M$. A theorem of Abramovic [1] on lattice operations of $\mathcal L_b(L,M )$ is generalized on Riesz spaces $L$ in which a weak form of Freudenthal's spectral theorem [4] holds.

scholarly journals The dual of the space of bounded operators on a Banach space

2021 ◽  
Vol 8 (1) ◽  
pp. 48-59
Author(s):  
Fernanda Botelho ◽  
Richard J. Fleming
Keyword(s):  
Banach Space ◽  
Tensor Product ◽  
Banach Spaces ◽  
Dual Space ◽  
Tensor Products ◽  
Bounded Operators ◽  
Projective Tensor Product ◽  
Projective Tensor

Abstract Given Banach spaces X and Y, we ask about the dual space of the 𝒧(X, Y). This paper surveys results on tensor products of Banach spaces with the main objective of describing the dual of spaces of bounded operators. In several cases and under a variety of assumptions on X and Y, the answer can best be given as the projective tensor product of X ** and Y *.

scholarly journals Correction to: Disjointness preserving operators on normed pre-Riesz spaces: extensions and inverses

Positivity ◽  
2020 ◽  
Vol 24 (2) ◽  
pp. 505-505
Author(s):  
Anke Kalauch ◽  
Onno van Gaans ◽  
Feng Zhang
Keyword(s):  
Riesz Spaces ◽  
Disjointness Preserving

scholarly journals The spectral theorem for well-bounded operators

1993 ◽  
Vol 54 (3) ◽  
pp. 334-351 ◽  
Author(s):  
Ian Doust ◽  
Qiu Bozhou
Keyword(s):  
Functional Calculus ◽  
Continuous Functions ◽  
Weak Compactness ◽  
Compact Interval ◽  
Spectral Theorem ◽  
Type B ◽  
Bounded Operators ◽  
Absolutely Continuous Functions ◽  
Absolutely Continuous

AbstractWell-bounded operators are those which possess a bounded functional calculus for the absolutely continuous functions on some compact interval. Depending on the weak compactness of this functional calculus, one obtains one of two types of spectral theorem for these operators. A method is given which enables one to obtain both spectral theorems by simply changing the topology used. Even for the case of well-bounded operators of type (B), the proof given is more elementary than that previously in the literature.

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