The aim is to improve the operability of an advanced demonstration platform incorporating reflexive teleoperated control concepts developed on a mobile robot system. The robot is capable of autonomously navigating in semi-structured environments. Reflexive tele-operation mode employs the robot extensive onboard sensor suite to prevent collisions with obstacles when the human operator assumes co...

A matrix $Pintextmd{C}^{ntimes n}$ is called a generalized reflection matrix if $P^{H}=P$ and $P^{2}=I$‎. ‎An $ntimes n$‎ ‎complex matrix $A$ is said to be a reflexive (anti-reflexive) matrix with respect to the generalized reflection matrix $P$ if $A=PAP$ ($A=-PAP$)‎. ‎In this paper‎, ‎we introduce two iterative methods for solving the pair of matrix equations $AXB=C$ and $DXE=F$ over reflexiv...

We prove that the notions of finite strict singularity, strict singularity and weak compactness coincide for operators defined on various spaces: the disc algebra, subspaces of C(K) with reflexive annihilator and subspaces of the Morse-TransueOrlicz space Mq (Ω, μ) with q > 2.

We present a terminating tableau system for the modal logic K∗. K∗ extends the basic modal logic K with a reflexive transitive closure operator for relations and is a proper fragment of propositional dynamic logic. We investigate two different approaches to achieve termination, namely chain-based blocking and pattern-based blocking. Pattern based-blocking has not been applied to a modal logic w...

A new example of a non-zero quasi-nilpotent operator T with reflexive commutant is presented. Norms ‖T n‖ converge to zero arbitrarily fast. Let H be a complex separable Hilbert space and let B(H) denote the algebra of all continuous linear operator on H. If T ∈ B(H) then {T}′ = {A ∈ B(H) : AT = TA} is called the commutant of T . By a subspace we always mean a closed linear subspace. If A ⊂ B(H...

Two unital dual operator algebras A,B are called ∆-equivalent if there exists an equivalence functor F : AM → BM which “extends” to a ∗−functor implementing an equivalence between the categories ADM and BDM. Here AM denotes the category of normal representations of A and ADM denotes the category with the same objects as AM and ∆(A)-module maps as morphisms (∆(A) = A ∩A ). We prove that any such...

In this paper, we first characterize reflexive one-sided A -submodules U of a unital operator algebra A in B(H ) completely. Furthermore we investigate the invariant subspace lattice Lat R and the reflexive hull Ref R, where R is the submodule generated by rank-one operators in U ; in particular, if L is a subspace lattice, we obtain when the rank-one algebra R of Alg L is big enough to determi...