Two conditional expectations in unbounded operator algebras (O∗-algebras) are discussed. One is a vector conditional expectation defined by a linear map of an O∗-algebra into the Hilbert space on which the O∗-algebra acts. This has the usual properties of conditional expectations. This was defined by Gudder and Hudson. Another is an unbounded conditional expectation which is a positive linear m...

The Kalman filter computes the maximum a posteriori (MAP) estimate of the states for linear state space models with Gaussian noise. We interpret the Kalman filter as the solution to a convex optimization problem, and show that we can generalize the MAP state estimator to any noise with log-concave density function and any combination of linear equality and convex inequality constraints on the s...

where φ : A → B(H) is a unital completely positive linear map from a C-algebra A to linear operators on a Hilbert space H, and x is a self-adjoint element in A with spectrum in I. Subsequently M. D. Choi [3] noted that it is enough to assume that φ is unital and positive. In fact, the restriction of φ to the commutative C-algebra generated by x is automatically completely positive by a theorem ...

The Kalman filter computes the maximum a posteriori (MAP) estimate of the states for linear state space models with Gaussian noise. We interpret the Kalman filter as the solution to a convex optimization problem, and show that we can generalize the MAP state estimator to any noise with log-concave density function and any combination of linear equality and convex inequality constraints on the s...

Let D be a non empty set, let us consider k, and let M be a matrix over D. Then M k is a matrix over D. We now state four propositions: (3) For every finite sequence M such that lenM = n+1 holds len(M n+1) = n: (4) Let M be a matrix over D of dimension n+1 m and M1 be a matrix over D. Then (i) if n > 0; then widthM = width(M n+1); and (ii) if M1 = hM(n+1)i; then widthM = widthM1: (5) For every ...

We characterize the infinitesimal generator of a semigroup of linear fractional self-maps of the unit ball in C, n ≥ 1. For the case n = 1 we also completely describe the associated Koenigs function and we solve the embedding problem from a dynamical point of view, proving, among other things, that a generic semigroup of holomorphic self-maps of the unit disc is a semigroup of linear fractional...

This investigation, in Bishop’s constructive mathematics in sense of well-known books [2], [3], [6] and Romano’s papers [9]-[15], is continuation of forthcoming Crvenkovic, Mitrovic and Romano’s paper [4], and the Romano’s paper [16]. Bishop’s constructive mathematics is developed on Constructive logic (or Intuitionistic logic ([19])) logic without the Law of Excluded Middle P ∨¬¬P . Let us not...

For two algebras $A$ and $B$, a linear map $T:A longrightarrow B$ is called separating, if $xcdot y=0$ implies $Txcdot Ty=0$ for all $x,yin A$. The general form and the automatic continuity of separating maps between various Banach algebras have been studied extensively. In this paper, we first extend the notion of separating map for module case and then we give a description of a linear se...

Let B be a real vector lattice and a Banach space under a semimonotonic norm. Suppose T is a linear operator on B which is positive and eventually compact, y is a positive vector, and A is a positive real. It is shown that (XI—TY1y is positive if, and only if, y is annihilated by the absolute value of any generalized eigenvector of T* associated with a strictly positive eigenvalue not less than...