Characterization of Riesz Spaces with Topologically Full Center

2013-07-26
Alpay, Safak
Orhon, Mehmet
Let E be a Riesz space and let E-similar to denote its order dual. The orthomorphisms Orth(E) on E, and the ideal center Z(E) of E, are naturally embedded in Orth(E-similar to) and Z(E-similar to) respectively. We construct two unital algebra and order- continuous Riesz homomorphisms.

Suggestions

Equivariant vector fields on three dimensional representation spheres
Gürağaç, Hami Sercan; Önder, Mustafa Turgut; Department of Mathematics (2011)
Let G be a finite group and V be an orthogonal four-dimensional real representation space of G where the action of G is non-free. We give necessary and sufficient conditions for the existence of a G-equivariant vector field on the representation sphere of V in the cases G is the dihedral group, the generalized quaternion group and the semidihedral group in terms of decomposition of V into irreducible representations. In the case G is abelian, where the solution is already known, we give a more elementary so...
Some finite-dimensional backward shift-invariant subspaces in the ball and a related factorization problem
Alpay, D; Kaptanoglu, HT (2000-12-15)
Beurling's theorem characterizes subspaces of the Hardy space invariant under the forward-shift operator in terms of inner functions. In this Note we consider the case where the ball replaces the open unit desk and the reproducing kernel Hilbert space with reproducing kernel 1/(1-Sigma (N)(1) a(j)w(j)*) replaces the Hardy space. We give explicit formulas which generalize Blaschke products in the case of spaces of finite codimension. (C) 2000 Academie des sciences/Editions scientifiques et medicales Elsevier...
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.
Equivariant cross sections of complex Stiefel manifolds
Onder, T (Elsevier BV, 2001-01-16)
Let G be a finite group and let M be a unitary representation space of G. A solution to the existence problem of G-equivariant cross sections of the complex Stiefel manifold W-k(M) of unitary k-frames over the unit sphere S(M) is given under mild restrictions on G and on fixed point sets. In the case G is an even ordered group, some sufficient conditions for the existence of G-equivariant real frame fields on spheres with complementary G-equivariant complex structures are also obtained, improving earlier re...
A characterization of an order ideal in Riesz spaces
Alpay, S; Emel'yanov, EY; Ercan, Z (American Mathematical Society (AMS), 2004-01-01)
In this paper we give a characterization of order ideals in Riesz spaces.
Citation Formats
S. Alpay and M. Orhon, “Characterization of Riesz Spaces with Topologically Full Center,” 2013, p. 35, Accessed: 00, 2020. [Online]. Available: https://hdl.handle.net/11511/65469.