Operator Hilbert Systems

Dosi, A.
The present note deals with operator Hilbert systems, which are quantizations of unital cones in Hilbert spaces. One central result of the note is that the Pisier operator Hilbert space is an operator system whose quantum cone of positive elements is described in terms of the quantum ball of the relevant conjugate Hilbert space. Finally, we obtain a solution to the problem of Paulsen, Todorov and Tomforde on separable morphisms between operator systems and characterize minmax- completely positive maps between Archimedean order unit spaces.


Finite type points on subsets of C-n
Yazıcı, Özcan (Elsevier BV, 2020-07-01)
In [4], D'Angelo introduced the notion of points of finite type for a real hypersurface M subset of C-n and showed that the set of points of finite type in M is open. Later, Lamel-Mir [8] considered a natural extension of D'Angelo's definition for an arbitrary set M subset of C-n. Building on D'Angelo's work, we prove the openness of the set of points of finite type for any subset M subset of C-n.
Seven, Ahmet İrfan (American Mathematical Society (AMS), 2016-11-01)
There is a well-known analogy between cluster algebras and Kac-moody algebras: roughly speaking, Kac-Moody algebras are associated with symmetrizable generalized Cartan matrices while cluster algebras correspond to skew-symmetrizable matrices. In this paper, we study an interplay between these two classes of matrices. We obtain relations in the Weyl groups of Kac-Moody algebras that come from mutation classes of skew-symmetrizable matrices. More precisely, we establish a set of relations satisfied by the re...
A strange recursion operator for a new integrable system of coupled Korteweg-de Vries equations
Karasu, A; Karasu, Atalay; Sakovich, SY (Springer Science and Business Media LLC, 2004-08-01)
A recursion operator is constructed for a new integrable system of coupled Korteweg de Vries equations by the method of gauge-invariant description of zero-curvature representations. This second-order recursion operator is characterized by unusual structure of its nonlocal part.
Integral criteria for oscillation of third order nonlinear differential equations
AKTAŞ, MUSTAFA FAHRİ; Tiryaki, Aydın; Zafer, Ağacık (Elsevier BV, 2009-12-15)
In this paper we are concerned with the oscillation of third order nonlinear differential equations of the form
Differential equations with state-dependent piecewise constant argument
Akhmet, Marat (Elsevier BV, 2010-06-01)
A new class of differential equations with state-dependent piecewise constant argument is introduced. It is an extension of systems with piecewise constant argument. Fundamental theoretical results for the equations the existence and uniqueness of solutions, the existence of periodic solutions, and the stability of the zero solution are obtained. Appropriate examples are constructed.
Citation Formats
A. Dosi, “Operator Hilbert Systems,” FUNCTIONAL ANALYSIS AND ITS APPLICATIONS, pp. 143–148, 2019, Accessed: 00, 2020. [Online]. Available: https://hdl.handle.net/11511/63386.