We study the duality properties of the well-known DFJP factorization of operators 3] by means of a reenement of it. Given an operator T : X ! Y we consider a decomposition T = jU k , where U : E ! F is an isomorphism, and j , U k are the factors in the DFJP factorization. If T is the conjugate operator of T , and T : X =X ! Y =Y is the operator given by T (x + X) := T x + Y (x 2 X), then we sho...

The hyperbolic algebra A h , studied recently by Katavolos and Power [5], is the weak star closed operator algebra on L 2 (R) generated by H ∞ (R), as multiplication operators, and by the dilation operators V t , t ≥ 0, given by V t f (x) = e t/2 f (e t x). We show that A h is a reflexive operator algebra and that the four dimensional manifold Lat A h (with the natural topology) is the reflexiv...

A Banach space X has the approximation property if and only if every compact set in X is in the range of a one-to-one bounded linear operator from a space that has a Schauder basis. Characterizations are given for Lp spaces and quotients of Lp spaces in terms of covering compact sets in X by operator ranges from Lp spaces. A Banach space X is a L1 space if and only if every compact set in X is ...

A necessary and sufficient condition on the support of a generic unmixed bivariate polynomial system is identified such that for polynomial systems with such support, the Dixon resultant formulation produces their resultants. It is shown that Sylvester-type matrices, called Dixon dialytic matrices, can also be obtained for such polynomial systems. These results are shown to be a generalization ...

this study was conducted to assess the in vitro organic matter digestibility (omd) of pistachio hull using rumen fluid of taleshi sheep. animals were fed diets composed of 34% pistachio hull, 29% grape pomace, 32% alfalfa, and 5% grain barley. the chemical composition and phenolics' levels of pistachio hull, either industrially dried pistachio hull (idph) or sun dried pistachio hull (sdph)...

Starting from Rodrigues formula we present a general construction of raising and lowering operators for orthogonal polynomials of continuous and discrete variable on uniform lattice. In order to have these operators mutually adjoint we introduce orthonormal functions with respect to the scalar product of unit weight. Using the Infeld-Hull factorization method, we generate from the raising and l...

Following [13] we provide new formulas for the Fenchel subdifferential of the conjugate of functions defined on locally convex spaces. In particular, this allows deriving expressions for the minimizers set of the lower semicontinuous convex hull of such functions. These formulas are written by means of primal objects related to the subdifferential of the initial function, namely a new enlargeme...

Standard binary subdivision operators may generate surfaces with unbounded curvatures at points corresponding to extraordinary vertices. This defect can be removed by manipulating the eigenvalues of the subdivision operator to impose a bounded curvature spectrum. This procedure may enlarge the support of an extraordinary vertex beyond its two-ring. In the ternary subdivision setting, where mesh...

1.1 Definitions We say a set S ⊆ Rd is convex if for any two points x,x′ ∈ S, the line segment conv{x,x′} := {(1−α)x+αx′ : α ∈ [0, 1]} between x and x′ (also called the convex hull of {x,x′}) is contained in S. Overloading terms, we say a function f : S → R is convex if its epigraph epi(f) := {(x, t) ∈ S × R : f(x) ≤ t} is a convex set (in Rd × R). Proposition 1. A function f : S → R is convex ...

We discuss the spectral subspace perturbation problem for a selfadjoint operator. Assuming that the convex hull of a part of its spectrum does not intersect the remainder of the spectrum, we establish an a priori sharp bound on variation of the corresponding spectral subspace under off-diagonal perturbations. This bound represents a new, a priori, tanΘ Theorem. We also extend the Davis–Kahan ta...