We study Riemannian or pseudo-Riemannian manifolds which carry the space of closed conformal vector fields of at least 2-dimension. Subject to the condition that at each point the set of closed conformal vector fields spans a non-degenerate subspace of the tangent space at the point, we prove a global and a local classification theorems for such manifolds.

Let X be a completely regular topological space, B(X) the Banach space of real-valued bounded continuous functions on X, with the usual norm ||&|| =supa?£x|&(#)| • A subset GCB(X) is called completely regular (c.r.) over X if given any closed subset KQ.X and point XoÇzX — K, there exists a ô £ G such that &(#o) = |NI a n ( i sup^^is: \b(x)\ <||&||. A topological space X is completely regular in...

We will extend the main result of [1] to non-unital case with a totally different proof. More precisely, we give an abstract characterization arbitrary self-adjoint weak⁎-closed subspace L(H) (equipped induced matrix norm, cone and weak⁎-topology). In order do this, analogue Bonsall for ⁎-operator spaces equipped closed cones.

Proof. Suppose that U1, . . . , Um are invariant subspaces of T ∈ L(V ). We wish to show that U1 + · · ·+ Um is also an invariant subspace. Consider any ~v ∈ U1 + · · ·+ Um. By definition, we can write ~v = ~u1 + · · ·+ ~um, for some ~u1 ∈ U1, . . . , ~um ∈ Um. Since U1, . . . , Um are invariant subspaces, by definition, we know T~u1 ∈ U1 ⊂ U1 + · · ·+ Um, ..., T~um ∈ Um ⊂ U1 + · · ·+ Um. Hence...

Convex-concave sets and Arnold hypothesis. The notion of convexity is usually defined for subsets of affine spaces, but it can be generalized for subsets of projective spaces. Namely, a subset of a projective space RP is called convex if it doesn’t intersect some hyperplane L ⊂ RP and is convex in the affine space RP \L. In the very definition of the convex subset of a projective space appears ...

This paper deals with an optimal instrumental variable method dedicated to subspace-based closed-loop system identification. The presented solution is based on the MOESP technique but requires to modify the original scheme by proposing a new PO MOESP method which uses reconstructed past input and past output data as instrumental variables. The developed approach is then illustrated via a simula...

We study the general discrete-time algebraic Riccati equation and deal with the case where the closed loop matrix corresponding to an arbitrary solution is singular. In this case the extended symplectic pencil associated with the DARE has 0 as a characteristic root and the corresponding spectral deflating subspace gives rise to a subspace where all solutions of the DARE coincide. This allows fo...

Let L be a closed subspace of C(X) which separates points and contains the constants. Denote the Korovkin closure of L by L̂. Then L = L̂ ∩ ML where ML = {f ∈ C(X) : ∫ f d(μ ◦ j) = 0 for all boundary dependences μ on KL}. We consider the relation between L and ML, the Choquet boundary of ML and the state space of ML. 1980 AMS Mathematics Subject Classification (1985 Revision): Primary 47B38, 47B5...

In this paper, we show that the consistency of closed-loop subspace identi cation methods (SIMs) can be achieved through innovation estimation. Based on this analysis, a su cient condition for the consistency of a new proposed closed-loop SIM is given, A consistent estimate of th Kalman gain under closed-loop conditions is also provided based on the algorithm. A multi-input-multi-output simulat...

We extend the Gaussian scale mixture model of dependent subspace source densities to include non-radially symmetric densities using Generalized Gaussian random variables linked by a common variance. We also introduce the modeling of skew in source densities and subspaces using a generalization of the Normal Variance-Mean mixture model. We give closed form expressions for subspace likelihoods an...