• Journal of the Korean Mathematical Society
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• v.59 no.4
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• pp.789-804
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• 2022

Striking result of Vybíral [51] says that Schur product of positive matrices is bounded below by the size of the matrix and the row sums of Schur product. Vybíral used this result to prove the Novak's conjecture. In this paper, we define Schur product of matrices over arbitrary C^*-algebras and derive the results of Schur and Vybíral. As an application, we state C^*-algebraic version of Novak's conjecture and solve it for commutative unital C^*-algebras. We formulate Pólya-Szegő-Rudin question for the C^*-algebraic Schur product of positive matrices.

• Kyungpook Mathematical Journal
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• v.57 no.4
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• pp.641-649
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• 2017

For partitioned matrices, the Khatri-Rao product is viewed as a generalized Hadamard product. In this paper we present Oppenheim's and Schur's determinantal inequalities for the Khatri-Rao product of two positive semidefinite matrices.

• Journal of the Korean Mathematical Society
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• v.38 no.1
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• pp.77-85
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• 2001

If an Azumaya algebra A is a homomorphic image of a finite group ring RG where G is a direct product of subgroups then A can be decomposed into subalgebras A(sub)i which are homomorphic images of subgroup rings of RG. This result is extended to projective Schur algebras, and in this case behaviors of 2-cocycles will play major role. Moreover considering the situation that A is represented by Azumaya group ring RG, we study relationships between the representing groups for A and A(sub)i.

• Journal of the Korean Mathematical Society
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• v.45 no.2
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• pp.313-329
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• 2008

In this paper, we study duality in the absolute Schur algebras that were first introduced in [1] and extended in [5]. This is done in a way analogous to the classical Schatten's Theorem on the Banach space $B(l_2)$ of bounded linear operators on $l_2$ involving the duality relation among the class of compact operators K, the trace class $C_1$ and $B(l_2)$. We also study the reflexivity in such the algebras.

• Journal of applied mathematics & informatics
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• v.25 no.1_2
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• pp.415-424
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• 2007

The generalized inverses have many important applications in the aspects of theoretic research and numerical computations and therefore they were studied by many authors. In this paper we get some necessary and sufficient conditions of the forward order law for {1}-inverse of multiple matrices products $A\;=\;A_1A_2{\cdots}A_n$ by using the maximal rank of generalized Schur complement.

• Journal of the Korean Mathematical Society
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• v.51 no.2
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• pp.345-362
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• 2014

We describe the Haagerup tensor product ${\ell}^{\infty}{\otimes}_h{\ell}^{\infty}$ and the extended Haagerup tensor product ${\ell}^{\infty}{\otimes}_{eh}{\ell}^{\infty}$ in terms of Schur product maps, and show that ${\ell}^{\infty}{\otimes}_h{\ell}^{\infty}{\cap}\mathbb{B}({\ell}^2)$(resp. ${\ell}^{\infty}{\otimes}_{eh}{\ell}^{\infty}{\cap}\mathbb{B}({\ell}^2)$) coincides with $c_0{\otimes}_hc_0{\cap}\mathbb{B}({\ell}^2)$(resp. $c_0{\otimes}_{eh}c_0{\cap}\mathbb{B}({\ell}^2)$). For $C^*2$-algebras A, B, it is shown that $A{\otimes}_hB=A{\otimes}_{eh}B$ if and only if A or B is finite-dimensional.

• Communications of the Korean Mathematical Society
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• v.12 no.3
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• pp.571-577
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• 1997

We first show that if $\psi : M_n(B(H)) \to M_n (B(H))$ is a $D_n \otimes F(H)$-bimodule map, then there is a matrix $A \in M_n$ such that $\psi = S_A$. Secondly, we show that for an operator space $\varepsilon, A \in M_n$, the Schur product map $S_A : M_n(\varepsilon) \to M_n(\varepsilon)$ and $\phi_A : M_n(\varepsilon) \to \varepsilon$, defined by $\phi_A([x_{ij}]) = \sum^{n}_{i,j=1}{a_{ij}x_{ij}}$, we have $\Vert S_A \Vert = \Vert S_A \Vert_{cb} = \Vert A \Vert_S, \Vert \phi_A \Vert = \Vert \phi_A \Vert_{cb} = \Vert A \Vert_1$ and obtain some characterizations of A for which $S_A$ is contractive.

• Communications of the Korean Mathematical Society
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• v.20 no.1
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• pp.35-49
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• 2005

For an extension field K of k, a restriction homomorphism on Brauer k-group B(k) maps Brauer k-algebras to Brauer K- algebras by tensor product. A purpose of this work is to study the restriction map that sends radical (Schur) k-algebras to radical (Schur) K-algebras. And we ask an analogous question with respect to corestriction map on Brauer group B(K) that whether the corestriction map sends radical K-algebras to radical k-algebras.

• Communications of the Korean Mathematical Society
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• v.11 no.3
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• pp.547-555
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• 1996

In this paper, we shall study the generalized covering group which plays a role for Schur multiplier. We discuss the lifting property over covering group and product of covering groups.

• Communications of the Korean Mathematical Society
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• v.18 no.4
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• pp.615-620
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• 2003

Semi-meet-prime projective modules and fully invariant meet-prime submodules of a projective module are studied. Actually a generalization of the Schur's lemma and semi-prime endmorphism rings of projective modules are considered.