Minh Toan Ho - Academia.edu (original) (raw)

Papers by Minh Toan Ho

A class of unital diagonal AH algebras will be studied in this paper. The density property of the... more A class of unital diagonal AH algebras will be studied in this paper. The density property of the set of all elements which are nilpotent up to (left and right multiple) unitaries is presented. As a consequence, these algebras have stable rank one. Section 3 also shows that an algebra in this class has the property LP (i.e., the linear span of projections is dense) provided a certain condition. Finally, restricting our attention to a special subclass which includes Villadsen algebras of the first type, we give the necessary and sufficient condition of real rank zero.

Banach Journal of Mathematical Analysis, 2015

Using a 'local' integral representation of a matrix connection of order n corresponding to an int... more Using a 'local' integral representation of a matrix connection of order n corresponding to an interpolation function of the same order, for each integer n, we can describe an injective map from the class of matrix connections of order n to the class of positive n-monotone functions on (0, ∞) and the range of this corresponding covers the class of interpolation functions of order 2n. In particular, the space of symmetric connections is isomorphic to the space of symmetric positive n-monotone functions. Moreover, we show that, for each n, the class of n-connections extremely contains that of (n + 2)-connections.

Linear Algebra and its Applications, 2013

A generalization of Powers-Størmer's inequality for operator monotone functions on [0, +∞) and fo... more A generalization of Powers-Størmer's inequality for operator monotone functions on [0, +∞) and for positive linear functional on general C *-algebras will be proved. It also will be shown that the generalized Powers-Størmer inequality characterizes the tracial functionals on C *-algebras.

Abstract and Applied Analysis, 2013

In the first part of this paper, we show that an AH algebraA=lim→(Ai,ϕi)has the LP property if an... more In the first part of this paper, we show that an AH algebraA=lim→(Ai,ϕi)has the LP property if and only if every element of the centre ofAibelongs to the closure of the linear span of projections inA. As a consequence, a diagonal AH-algebra has the LP property if it has small eigenvalue variation in the sense of Bratteli and Elliott. The second contribution of this paper is that for an inclusion of unitalC*-algebrasP⊂Awith a finite Watatani index, if a faithful conditional expectationE:A→Phas the Rokhlin property in the sense of Kodaka et al., thenPhas the LP property under the condition thatAhas the LP property. As an application, letAbe a simple unitalC*-algebra with the LP property,αan action of a finite groupGontoAut(A). Ifαhas the Rokhlin property in the sense of Izumi, then the fixed point algebraAGand the crossed product algebraA ⋊α Ghave the LP property. We also point out that there is a symmetry on the CAR algebra such that its fixed point algebra does not have the LP prope...

Advances in Geometry, 2016

A concept of nondegenerate basic closed semi-algebraic sets in ℝnis introduced. These areunbounde... more A concept of nondegenerate basic closed semi-algebraic sets in ℝnis introduced. These areunboundedclosed semi-algebraic sets for which we obtain some representations of polynomials with positive infima (the polynomials are further assumed to be bounded ifn>2) and solutions of the moment problem. The key to obtain these results is an explicit description of the algebra of bounded polynomials on a nondegenerate basic semi-algebraic set via the combinatorial information of the Newton polyhedron corresponding to the generators of the semi-algebraic set.

arXiv: Algebraic Geometry, 2019

In this paper we establish some applications of the Scherer-Hol's theorem for polynomial matr... more In this paper we establish some applications of the Scherer-Hol's theorem for polynomial matrices. Firstly, we give a representation for polynomial matrices positive definite on subsets of compact polyhedra. Then we establish a Putinar-Vasilescu Positivstellensatz for homogeneous and non-homogeneous polynomial matrices. Next we propose a matrix version of the Polya-Putinar-Vasilescu Positivstellensatz. Finally, we approximate positive semi-definite polynomial matrices using sums of squares.

Positivity, 2021

In this paper we establish some Positivstellensatze for polynomial matrices, applying the Scherer... more In this paper we establish some Positivstellensatze for polynomial matrices, applying the Scherer–Hol theorem. Firstly, we give a representation for polynomial matrices positive definite on subsets of compact polyhedra. Then we establish a Putinar-Vasilescu Positivstellensatz for polynomial matrices. Next we propose a matrix version of the Dickinson–Povh Positivstellensatz. Finally, we establish a version of Marshall’s theorem for polynomial matrices, approximating positive semi-definite polynomial matrices using sums of squares.

Mathematical Inequalities & Applications, 2019

In this paper we show that for a non-negative operator monotone function f on [0, ∞) such that f ... more In this paper we show that for a non-negative operator monotone function f on [0, ∞) such that f (0) = 0 and for any positive semidefinite matrices A and B, Tr ((A − B)(f (A) − f (B))) ≤ Tr (|A − B|f (|A − B|)). When the function f is operator convex on [0, ∞), the inequality is reversed.

Journal of Functional Analysis, 2009

We study the limits of inductive sequences (A i , φ i) where each A i is a direct sum of full mat... more We study the limits of inductive sequences (A i , φ i) where each A i is a direct sum of full matrix algebras over compact metric spaces and each partial map of φ i is diagonal. We give a new characterisation of simplicity for such algebras, and apply it to prove that the said algebras have stable rank one whenever they are simple and unital. Significantly, our results do not require any dimension growth assumption.