• Honam Mathematical Journal
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• v.26 no.1
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• pp.61-75
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• 2004

It is shown that every almost linear mapping $h:{\mathcal{A}}{\rightarrow}{\mathcal{B}}$ of a unital Poisson Banach algebra ${\mathcal{A}}$ to a unital Poisson Banach algebra ${\mathcal{B}}$ is a Poisson algebra homomorphism when h(xy) = h(x)h(y) holds for all $x,y{\in}\;{\mathcal{A}}$, and that every almost linear almost multiplicative mapping $h:{\mathcal{A}}{\rightarrow}{\mathcal{B}}$ is a Poisson algebra homomorphism when h(qx) = qh(x) for all $x\;{\in}\;{\mathcal{A}}$. Here the number q is in the functional equation given in the almost linear almost multiplicative mapping. We prove that every almost Poisson bracket $B:{\mathcal{A}}\;{\times}\;{\mathcal{A}}\;{\rightarrow}\;{\mathcal{A}}$ on a Banach algebra ${\mathcal{A}}$ is a Poisson bracket when B(qx, z) = B(x, qz) = qB(x, z) for all $x,z{\in}\;{\mathcal{A}}$. Here the number q is in the functional equation given in the almost Poisson bracket.

• Journal of the Chungcheong Mathematical Society
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• v.8 no.1
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• pp.37-44
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• 1995

In this paper we show that every left derivation on a semiprime Banach algebra A is a derivation which maps A into the intersection of the center of A and the Jacobson radical of A, and hence every left derivation on a semisimple Banach algebra is zero.

• Journal of the Korean Mathematical Society
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• v.50 no.6
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• pp.1349-1367
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• 2013

The weighted Moore-Penrose inverse will be introduced and studied in the context of Banach algebras. In addition, weighted EP Banach algebra elements will be characterized. The Banach space operator case will be also considered.

• Journal of the Chungcheong Mathematical Society
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• v.24 no.2
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• pp.221-238
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• 2011

We prove the Hyers-Ulam stability of generalized Jensen's equations in Banach modules over a unital $C^{\ast}$-algebra. It is applied to show the stability of generalized Jensen's equations in a Hilbert module over a unital $C^{\ast}$-algebra. Moreover, we prove the stability of linear operators in a Hilbert module over a unital $C^{\ast}$-algebra.

• Journal of applied mathematics & informatics
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• v.28 no.1_2
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• pp.233-241
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• 2010

In this paper, we investigate the following functional inequality $${\parallel}f(\frac{x\;+\;y}{2}\;+\;z)\;+\;f(\frac{x\;+\;y}{2}\;+\;y)\;+\;f(\frac{y\;+\;z}{2}\;+\;x){\parallel\;\leq\;\parallel}2f(x\;+\;y\;+\;z)\parallel$$ in Banach modules over a $C^*$-algebra, and prove the generalized Hyers-Ulam stability of linear mappings in Banach modules over a $C^*$-algebra.

• Bulletin of the Korean Mathematical Society
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• v.40 no.1
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• pp.53-61
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• 2003

We prove the generalized Hyers-Ulam-Rassias stability of the invertible mapping in a Banach module over a unital Banach algebra, and prove the generalized Hyers-Ulam-Rassias stability of the Jensen's functional equations in a Hilbert module over a unital $C^{*}$-algebra.

• Korean Journal of Mathematics
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• v.27 no.2
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• pp.445-463
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• 2019

Let C[0, T] denote the space of continuous real-valued functions on [0, T]. On the space C[0, T], we introduce a Banach algebra of series of functions which are generalized Fourier-Stieltjes transforms of measures of finite variation on the product of simplex and Euclidean space. We evaluate analytic Feynman integrals of the functions in the Banach algebra which play significant roles in the Feynman integration theory and quantum mechanics.

• The Pure and Applied Mathematics
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• v.30 no.1
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• pp.15-24
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• 2023

In this paper, we show that bounded Hochschild homology and cohomology of associated matrix Banach algebra 𝔊(𝔄, R, S, 𝔅) to a Morita context 𝔐(𝔄, R, S, 𝔅, { }, [ ]) are isomorphic to those of the Banach algebra 𝔄. Consequently, we indicate that the n-amenability and simplicial triviality of 𝔊(𝔄, R, S, 𝔅) are equivalent to the n-amenability and simplicial triviality of 𝔄.

• Journal of the Chungcheong Mathematical Society
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• v.19 no.1
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• pp.9-18
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• 2006

In this paper, the completion of a quasi-normed algebra and the completion of a quasi-normed module over a Banach algebra are constructed.

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