scholarly journals Symmetry groups on ordered Banach spaces

1986 ◽  
Vol 33 (2) ◽  
pp. 177-187 ◽  
Author(s):  
Sadayuki Yamamuro
Keyword(s):  
Banach Space ◽  
Banach Spaces ◽  
Symmetry Groups ◽  
Ordered Banach Space ◽  
Group Of Symmetries ◽  
Ordered Banach Spaces

A symmetry of an ordered Banach space is an order and norm isomorphism which commutes with its ideal centre. A class of ordered Banach spaces is introduced to show that, for a space in this class, the group of symmetries is trivial if and only if the space is lattice-ordered. When this group becomes larger, the space approaches an antilattice. This phenomenon is also investigated.

scholarly journals Monotonic norms in ordered Banach spaces

1988 ◽  
Vol 45 (2) ◽  
pp. 217-219 ◽  
Author(s):  
K. F. Ng ◽  
C. K. Law
Keyword(s):  
Banach Space ◽  
Banach Spaces ◽  
Dual Space ◽  
Alternative Proof ◽  
Ordered Banach Space ◽  
Dual Result ◽  
Ordered Banach Spaces

AbstractLet B be an ordered Banach space with ordered Banach dual space. Let N denote the canonical half-norm. We give an alternative proof of the following theorem of Robinson and Yamamuro: the norm on B is α-monotone (α ≥ 1) if and only if for each f in B* there exists g ∈ B* with g ≥ 0, f and ∥g∥ ≤ α N(f). We also establish a dual result characterizing α-monotonicity of B*.

scholarly journals Common fixed point theorems for a pair of countably condensing mappings in ordered banach spaces

2003 ◽  
Vol 16 (3) ◽  
pp. 243-248 ◽  
Author(s):  
B. C. Dhage ◽  
Donal O'Regan ◽  
Ravi P. Agarwal
Keyword(s):  
Banach Space ◽  
Fixed Point ◽  
Common Fixed Point ◽  
Banach Spaces ◽  
Fixed Point Theorems ◽  
Ordered Banach Space ◽  
Isotone Mappings ◽  
Common Fixed Point Theorems ◽  
Ordered Banach Spaces

In this paper some common fixed point theorems for a pair of multivalued weakly isotone mappings on an ordered Banach space are proved.

scholarly journals Fixed Point Theorems in Ordered Banach Spaces and Applications to Nonlinear Integral Equations

2012 ◽  
Vol 2012 ◽  
pp. 1-15 ◽  
Author(s):  
Ravi P. Agarwal ◽  
Nawab Hussain ◽  
Mohamed-Aziz Taoudi
Keyword(s):  
Banach Space ◽  
Fixed Point ◽  
Common Fixed Point ◽  
Banach Spaces ◽  
Fixed Point Theorems ◽  
Ordered Banach Space ◽  
Nonlinear Integral Equations ◽  
Common Fixed Point Theorems ◽  
Ordered Banach Spaces ◽  
Nonlinear Mappings

We present some new common fixed point theorems for a pair of nonlinear mappings defined on an ordered Banach space. Our results extend several earlier works. An application is given to show the usefulness and the applicability of the obtained results.

scholarly journals Strongly exposed points in bases for the positive cone of ordered Banach spaces and characterizations of l1(Г)

1986 ◽  
Vol 29 (2) ◽  
pp. 271-282 ◽  
Author(s):  
Ioannis A. Polyrakis
Keyword(s):  
Banach Space ◽  
Banach Spaces ◽  
Convex Sets ◽  
Extreme Points ◽  
Positive Cone ◽  
Infinite Dimensional ◽  
Strongly Exposed Points ◽  
Nikodym Property ◽  
Choquet Theory ◽  
Ordered Banach Spaces

The study of extreme, strongly exposed points of closed, convex and bounded sets in Banach spaces has been developed especially by the interconnection of the Radon–Nikodým property with the geometry of closed, convex and bounded subsets of Banach spaces [5],[2] . In the theory of ordered Banach spaces as well as in the Choquet theory, [4], we are interested in the study of a special type of convex sets, not necessarily bounded, namely the bases for the positive cone. In [7] the geometry (extreme points, dentability) of closed and convex subsets K of a Banach space X with the Radon-Nikodým property is studied and special emphasis has been given to the case where K is a base for acone P of X. In [6, Theorem 1], it is proved that an infinite-dimensional, separable, locally solid lattice Banach space is order-isomorphic to l1 if, and only if, X has the Krein–Milman property and its positive cone has a bounded base.

Lattice Banach spaces, order-isomorphic to l1

1983 ◽  
Vol 94 (3) ◽  
pp. 519-522 ◽  
Author(s):  
Ioannis A. Polyrakis
Keyword(s):  
Banach Space ◽  
Banach Spaces ◽  
Positive Cone ◽  
Schauder Basis ◽  
Ordered Banach Space

It is known, (see [7], theorem 4 or [8], corollary II, 10.1), that a positive generated, ordered Banach space X is order-isomorphic to l1 iff X has a Schauder basis which generates its positive cone X+ and X+ has a bounded base.

scholarly journals Geometric Characterization of Injective Banach Lattices

Mathematics ◽  
2021 ◽  
Vol 9 (3) ◽  
pp. 250
Author(s):  
Anatoly Kusraev ◽  
Semën Kutateladze
Keyword(s):  
Banach Space ◽  
Unit Ball ◽  
Banach Spaces ◽  
Set Theory ◽  
Banach Lattice ◽  
Dual Space ◽  
Banach Lattices ◽  
Transfer Principle ◽  
Ordered Banach Spaces

This is a continuation of the authors’ previous study of the geometric characterizations of the preduals of injective Banach lattices. We seek the properties of the unit ball of a Banach space which make the space isometric or isomorphic to an injective Banach lattice. The study bases on the Boolean valued transfer principle for injective Banach lattices. The latter states that each such lattice serves as an interpretation of an AL-space in an appropriate Boolean valued model of set theory. External identification of the internal Boolean valued properties of the corresponding AL-spaces yields a characterization of injective Banach lattices among Banach spaces and ordered Banach spaces. We also describe the structure of the dual space and present some dual characterization of injective Banach lattices.

scholarly journals ON THE MONOTONE CONVERGENCE OF SOME ITERATIVE PROCEDURES IN PARTIALLY ORDERED BANACH SPACES

1990 ◽  
Vol 21 (3) ◽  
pp. 269-277
Author(s):  
IOANNIS K. ARGYROS
Keyword(s):  
Banach Space ◽  
Nonlinear Equation ◽  
Monotone Convergence ◽  
Ordered Banach Space ◽  
Algebraic Equations ◽  
Partially Ordered ◽  
Linear Algebraic Equations ◽  
Enclosure Methods ◽  
Iterative Procedures ◽  
Ordered Banach Spaces

We provide some enclosure methods for the solution of a nonlinear equation in a partially ordered Banach space. By using a certain projection operator we show that the solution can be obtained from the solution of a system of linear algebraic equations.

Fixed point theorems and convergence theorems for monotone (α, β)-nonexpansive mappings in ordered Banach spaces

2017 ◽  
Vol 26 (2) ◽  
pp. 163-180
Author(s):  
KHANITIN MUANGCHOO-I ◽  
DAWUD THONGTHA ◽  
POOM KUMAM ◽  
YEOL JE CHO
Keyword(s):  
Banach Space ◽  
Nonexpansive Mapping ◽  
Fixed Point Theorems ◽  
Existence Theorems ◽  
Nonexpansive Mappings ◽  
Ordered Banach Space ◽  
Weak And Strong Convergence ◽  
Convergence Theorems ◽  
Alpha Beta ◽  
Ordered Banach Spaces

In this paper, we introduce the notion of a monotone (\alpha,\beta)-nonexpansive mapping in an ordered Banach space E with the partial order \leq and prove some existence theorems of fixed points of a monotone (\alpha,\beta)-nonexpansive mapping in a uniformly convex ordered Banach space. Also, we prove some weak and strong convergence theorems of Ishikawa type iteration under the control condition \[\limsup_{n\to\infty}s_n(1-s_n) > 0\quad and \quad \liminf_{n\to\infty}s_n(1-s_n) > 0.\] Finally, we give an numerical example to illustrate the main result in this paper.

scholarly journals On linear operators on ordered banach spaces

1983 ◽  
Vol 27 (2) ◽  
pp. 285-305 ◽  
Author(s):  
Sadayuki Yamamuro
Keyword(s):  
Banach Space ◽  
Linear Operator ◽  
Positive Linear Operator ◽  
Linear Operators ◽  
Order Structure ◽  
Ordered Banach Space ◽  
Continuous Linear ◽  
Positive Unit ◽  
Ordered Banach Spaces ◽  
Continuous Linear Operators

The order structure of the space of all continuous linear operators on an ordered Banach space is studied. The main topic is the Robinson property, that is, the norm of a positive linear operator is attained on the positive unit cone.

scholarly journals Entire Analytic Functions of Unbounded Type on Banach Spaces and Their Lineability

Axioms ◽  
2021 ◽  
Vol 10 (3) ◽  
pp. 150
Author(s):  
Andriy Zagorodnyuk ◽  
Anna Hihliuk
Keyword(s):  
Banach Space ◽  
Banach Spaces ◽  
Analytic Functions ◽  
Entire Functions ◽  
Dimensional Algebra ◽  
Dimensional Banach Space ◽  
Infinite Dimensional ◽  
Linear Subspaces ◽  
Infinite Dimensional Banach Space

In the paper we establish some conditions under which a given sequence of polynomials on a Banach space X supports entire functions of unbounded type, and construct some counter examples. We show that if X is an infinite dimensional Banach space, then the set of entire functions of unbounded type can be represented as a union of infinite dimensional linear subspaces (without the origin). Moreover, we show that for some cases, the set of entire functions of unbounded type generated by a given sequence of polynomials contains an infinite dimensional algebra (without the origin). Some applications for symmetric analytic functions on Banach spaces are obtained.

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