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    Convexity and monotonicity of certain maps involving hadamard products and bochner integrals for continuous fields of operators
    (2019-10-30)
    We investigate the convexity and the monotonicity of certain maps involving Hadamard products and Bochner integrals for continuous fields of Hilbert space operators. Their special cases and consequences are then discussed. In particular, we obtain certain arithmetic mean-harmonic mean, Jensen, and Fiedler type inequalities.
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    Analytic properties of tracy-singh products for operator matrices
    (2018-01-01)
    Ploymukda, Arnon
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    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
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    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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    Kantorovich type integral inequalities for tensor products of continuous fields of positive operators
    (2018-01-01)
    This paper establishes a number of Kantorovich type integral inequalities involving tensor products of continuous fields of positive operators parametrized by a locally compact Hausdorff space. Such integrals appear as Bochner integrals with respect to a finite Radon measure on that space. Kantorovich type inequalities in which the operator product are replaced by an operator mean are also investigated.
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    Khatri-rao sums for hilbert space operators
    (2018-05-01)
    Ploymukda, Arnon
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    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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    Algebraic and order properties of tracy-singh products for operator matrices
    (2018-01-01)
    Ploymukda, Arnon
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    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.
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    Tracy-singh products and classes of operators
    (2019-07-01)
    Ploymukda, Arnon
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    Lewkeeratiyutkul, Wicharn
    We investigate relationship between Tracy-Singh products and certain classes of Hilbert space operators. We show that the normality, hyponormality, paranormality of operators are preserved by Tracy-Singh products. Operators of class-A type are also preserved under Tracy-Singh products. Moreover, we obtain necessary and sufficient conditions for the Tracy- Singh product of two operators to be normal, quasinormal, (co)isometry, and unitary.
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    Algebraic, order, and analytic properties of Tracy-Singh sums for Hilbert space operators
    (2019-07-01)
    Ploymukda, Arnon
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    We introduce the Tracy-Singh sum for operators on a Hilbert space, generalizing both the Tracy-Singh sum for matrices and the tensor sum for operators. The Tracy-Singh sum is shown to be compatible with algebraic operations and order relations. Then we establish a binomial theorem involving Tracy-Singh sums, and its consequences. We also investigate continuity, convergence, and norm bounds for Tracy-Singh sums. Moreover, we derive operator identities involving Tracy-Singh sums and certain operator functions defined by power series.