Let S be a subring of the ring R. We investigate the question of whether S ∩ U(R) = U(S) holds for the units. In many situations our answer is positive. There is a special emphasis on the case when R is a full matrix ring and S is a structural subring of R defined by a reflexive and transitive relation.

Let X be a compact Hausdorff space and let H be a separable Hilbert space. We prove that the group of all order automorphisms of the C∗-algebra C(X)⊗ B(H) is algebraically reflexive.

Smarandache initiated neutrosophic sets (NSs) which can be used as a mathematical tool for dealing with indeterminate and inconsistent information. In order to apply NSs conveniently, single valued neutrosophic sets (SVNSs) were proposed by Wang et al. In this paper, we propose single valued neutrosophic relations (SVNRs) and study their properties. The notions of anti-reflexive kernel, symmetr...

The pro and anti-saccade task (PAT) is a widely used tool in the study of overt and covert attention with promising potential role in neurocognitive and psychiatric assessment. However, specific PAT protocols can vary significantly between labs, potentially resulting in large variations in findings across studies. In light of recent calls towards a standardization of PAT the current study's obj...

We show that if the duality between a Banach space A and its anti-dual A* is given by the inner product of a Hilbert space H, then (A, A*)1/2,2 = H = (A,A*)[l,2~, provided A satisfies certain mild conditions. We do not assume A is reflexive. Applications are given to normed ideals of operators.

Tourette's syndrome is characterized by involuntary tics and, although the underlying pathogenesis and pathophysiology of Tourette's syndrome remains unclear, it is suspected that basal ganglia structures are involved. The basal ganglia also play an important role in the control of saccadic eye movements and we therefore hypothesize that Tourette's syndrome patients have abnormal control of sac...

In this note, generalized connections σT,f are investigated, where AσT,fB = TAfT − A (B) for positive semidefinite matrix A and hermitian matrix B, and operator monotone function f : J → R on an interval J ⊂ R. Here the symbol T A denotes a reflexive generalized inverse of a positive bounded linear operator TA. The problem of estimating a given generalized connection by other ones is studied. T...