Chansangiam, Pattrawut

Preferred name

Alternative Name

Chansangiam, P.

Main Affiliation

School of Science

pattrawut.ch@kmitl.ac.th

Now showing 1 - 10 of 17

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Weighted Lim’s geometric mean of positive invertible operators on a Hilbert space
(2020-03-01)
Ploymukda, Arnon
;
Chansangiam, Pattrawut
We generalize the weighted Lim’s geometric mean of positive definite matrices to positive invertible operators on a Hilbert space. This mean is defined via a certain bijection map and parametrized over Hermitian unitary operators. We derive an explicit formula of the weighted Lim’s geometric mean in terms of weighted metric/spectral geometric means. This kind of operator mean turns out to be a symmetric Lim-Pálfia weighted mean and satisfies the idempotency, the permutation invariance, the joint homogeneity, the self-duality, and the unitary invariance. Moreover, we obtain relations between weighted Lim geometric means and Tracy-Singh products via operator identities.
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Riccati equation and metric geometric means of positive semidefinite matrices involving semi-tensor products
(2023-01-01)
Chansangiam, Pattrawut
;
Ploymukda, Arnon
We investigate the Riccati matrix equation XA<sup>−1</sup>X = B in which the conventional matrix products are generalized to the semi-tensor products ⋉. When A and B are positive definite matrices satisfying the factor-dimension condition, this equation has a unique positive definite solution, which is defined to be the metric geometric mean of A and B. We show that this geometric mean is the maximum solution of the Riccati inequality. We then extend the notion of the metric geometric mean to positive semidefinite matrices by a continuity argument and investigate its algebraic properties, order properties and analytic properties. Moreover, we establish some equations and inequalities of metric geometric means for matrices involving cancellability, positive linear map and concavity. Our results generalize the conventional metric geometric means of matrices.
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Integral inequalities of chebyshev type for continuous fields of Hermitian operators involving Tracy-Singh products and weighted pythagorean means
(2019-10-01)
Ploymukda, Arnon
;
Chansangiam, Pattrawut
In this paper, we establish several integral inequalities of Chebyshev type for bounded continuous fields of Hermitian operators concerning Tracy-Singh products and weighted Pythagorean means. The weighted Pythagorean means considered here are parametrization versions of three symmetric means: the arithmetic mean, the geometric mean, and the harmonic mean. Every continuous field considered here is parametrized by a locally compact Hausdorff space equipped with a finite Radon measure. Tracy-Singh product versions of the Chebyshev-Grüss inequality via oscillations are also obtained. Such integral inequalities reduce to discrete inequalities when the space is a finite space equipped with the counting measure. Moreover, our results include Chebyshev-type inequalities for tensor product of operators and Tracy-Singh/Kronecker products of matrices.
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Jensen’s type inequalities involving tracy-singh products, khatri-rao products, tracy-singh sums and khatri-rao sums
(2020-01-01)
Ploymukda, Arnon
;
Chansangiam, Pattrawut
In this paper, we establish a number of Jensen’s type inequalities for Hilbert space operators involving convex/concave functions, unital positive linear maps, and certain operator products and sums. The products and sums considered here include the Tracy-Singh product, the Khatri-Rao products, the Tracy-Singh sum, and the Khatri-Rao sum. Moreover, we generalize Jensen’s type inequalities in term of functional calculus of two-variable functions. In particular, we obtain Kantorovich-type operator inequalities involving the products and sums.
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Analytic properties of tracy-singh products for operator matrices
(2018-01-01)
Ploymukda, Arnon
;
Chansangiam, Pattrawut
;
Lewkeeratiyutkul, Wicharn
We show that the Tracy-Singh product of Hilbert space operators is continuous with respect to the operator-norm topology. The Tracy-Singh product of two nonzero operators is compact if and only if both factors are compact. We provide upper and lower bounds for certain Schatten p-norms of the Tracy-Singh product of operators. It turns out that this product is continuous with respect to the topologies on norm ideals of compact operators, trace class operators, and Hilbert-Schmidt class operators. Thus the Tracy-Singh product preserves such classes of operators.
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Khatri-Rao products and selection operators
(2019-08-01)
Ploymukda, Arnon
;
Chansangiam, Pattrawut
We develop further theory for Khatri-Rao products of Hilbert space operators in connections with selection operators. We provide two constructions related to selection operators. Then we establish certain identities and inequalities involving Khatri-Rao and Tracy-Singh products. As consequences, we obtain some characterizations for the mixed product property concerning the Khatri-Rao product of operators.
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Khatri-rao sums for hilbert space operators
(2018-05-01)
Ploymukda, Arnon
;
Chansangiam, Pattrawut
We generalize the notions of Khatri-Rao sums for matrices and tensor sums for Hilbert space operators to Khatri-Rao sums for Hilbert space operators. This kind of operator sum is compatible with algebraic operations and order relations. We investigate its analytic properties, including continuity, convergence, and norm bounds. We also discuss the role of selection operator that relates Khatri-Rao sums to Tracy-Singh sums and Khatri-Rao products. Binomial theorem involving Khatri-Rao sums and its consequences are then established.
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Inequalities on weighted classical pythagorean means, Tracy-Singh products, and Khatri-Rao products for hermitian operators
(2020-03-01)
Ploymukda, Arnon
;
Chansangiam, Pattrawut
We establish a number of operator inequalities between three kinds of means, namely, weighted arithmetic/harmonic/geometric means, and two kinds of operator products, namely, Tracy-Singh products and Khatri-Rao products. In this study, we have validated the data under certain assumptions relying on (opposite) synchronization, comparability, and spectra of operators. The tensor product of operators, and Tracy-Singh/Khatri-Rao products of matrices as special cases are presented.
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Concavity and convexity of several maps involving Tracy-Singh products, Khatri-Rao products, and operator-monotone functions of positive operators
(2019-01-01)
Ploymukda, Arnon
;
Chansangiam, Pattrawut
We establish concavity and convexity theorems for a number of operator-valued maps involving Tracy-Singh products and Khatri-Rao products of positive operators on a Hilbert space. Operator means serve as useful tools for some convexity results. We also investigate certain maps dealing with positive operator-monotone functions. In this case, the concavity and the convexity of such maps are examined through suitable integral representations of the operator-monotone functions on the unit interval with respect to finite Borel measures.
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Algebraic and order properties of tracy-singh products for operator matrices
(2018-01-01)
Ploymukda, Arnon
;
Chansangiam, Pattrawut
;
Lewkeeratiyutkul, Wicharn
We generalize the tensor product for operators to the Tracy-Singh product for operator matrices acting on the direct sum of Hilbert spaces. This kind of operator product is compatible with algebraic operations and order relations for operators. It follows that this product preserves many structure properties of operators.

Chansangiam, Pattrawut

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