• Bulletin of the Korean Mathematical Society
• /
• v.54 no.2
• /
• pp.485-495
• /
• 2017

The aim of this paper is twofold. Firstly, we introduce the concept of semi-partial isometry in a Banach algebra and carry out a comparison and a classification study for this concept. In particular, we show that in the context of $C^*$-algebras this concept coincides with the notion of partial isometry. Our results encompass several earlier ones concerning partial isometries in Hilbert spaces, Banach spaces and $C^*$-algebras. Finally, we study the notion of (m, p)-semi partial isometries.

• Honam Mathematical Journal
• /
• v.32 no.2
• /
• pp.217-226
• /
• 2010

Using the Bu$\c{s}$neag's model ([1, 2, 3]), the notion of pseudo-valuations (valuations) on a ${\mathbf{BCK/BCI}}$-algebra is introduced, and a pseudo-metric is induced by a pseudo-valuation on ${\mathbf{BCK/BCI}}$-algebras. Based on the notion of (pseudo) valuation, we show that the binary operation in ${\mathbf{BCK/BCI}}$-algebras is uniformly continuous.

• Bulletin of the Korean Mathematical Society
• /
• v.49 no.2
• /
• pp.235-247
• /
• 2012

We study sufficient conditions for function algebras generated by four smooth functions on a small closed bidisk near the origin in $\mathbb{C}$ to coincide with the space of continuous functions on the bidisk. This problem in one dimension has been studied by De Paepe and the second name author.

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

• Kyungpook Mathematical Journal
• /
• v.60 no.1
• /
• pp.21-43
• /
• 2020

We introduce the Leavitt path algebras of ultragraphs and we characterize their ideal structures. We then use this notion to introduce and study the algebraic analogy of Exel-Laca algebras.

• Journal of the Chungcheong Mathematical Society
• /
• v.32 no.2
• /
• pp.195-205
• /
• 2019

We consider additive mappings similar to derivations on Banach ${\ast}$-algebras and we will first study the conditions for such additive mappings on Banach ${\ast}$-algebras. Then we prove some theorems concerning approximate linear mappings of derivation-type on Banach ${\ast}$-algebras. As an application, approximate linear mappings of derivation-type on $C^{\ast}$-algebra are characterized.

• East Asian mathematical journal
• /
• v.17 no.1
• /
• pp.33-45
• /
• 2001

In this paper an improved version of a fixed point theorem of the present author [3] in Banach algebras is obtained under the weaker conditions with a different method and using measure of non-compactness. The newly developed fixed point theorem is further-applied to certain nonlinear integral equations of mixed type for proving the existence theorems and stability of the solution in Banach algebras.

• Communications of the Korean Mathematical Society
• /
• v.38 no.4
• /
• pp.1019-1028
• /
• 2023

Let 𝔄 and 𝔅 be unital prime *-algebras such that 𝔄 contains a nontrivial projection. In the present paper, we show that if a bijective map Θ : 𝔄 → 𝔅 satisfies Θ(_*[X ⋄ Y, Z]) = _*[Θ(X) ⋄ Θ(Y), Θ(Z)] for all X, Y, Z ∈ 𝔄, then Θ or -Θ is a *-ring isomorphism. As an application, we shall characterize such maps in factor von Neumann algebras.

• Journal of the Korean Mathematical Society
• /
• v.50 no.1
• /
• pp.61-80
• /
• 2013

In this paper, we study ${\alpha}$-completely positive maps between locally $C^*$-algebras. As a generalization of a completely positive map, an ${\alpha}$-completely positive map produces a Krein space with indefinite metric, which is useful for the study of massless or gauge fields. We construct a KSGNS type representation associated to an ${\alpha}$-completely positive map of a locally $C^*$-algebra on a Krein locally $C^*$-module. Using this construction, we establish the Radon-Nikod$\acute{y}$m type theorem for ${\alpha}$-completely positive maps on locally $C^*$-algebras. As an application, we study an extremal problem in the partially ordered cone of ${\alpha}$-completely positive maps on a locally $C^*$-algebra.

• Journal of the Chungcheong Mathematical Society
• /
• v.19 no.2
• /
• pp.111-121
• /
• 2006

All d-homogeneous $C^*$-algebras $T^d$ over $\prod^{s_4}S^4{\times}\prod^{s_2}S^2{\times}\prod^{s_3}S^3{\times}\prod^{s_1}S^1$ are constructed. It is shown that $T^d$ are strongly Morita equivalent to $C(\prod^{s_4}S^4{\times}\prod^{s_2}S^2{\times}\prod^{s_3}S^3{\times}\prod^{s_1}S^1)$.