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PSEUDO JORDAN HOMOMORPHISMS AND DERIVATIONS ON MODULE EXTENSIONS AND TRIANGULAR BANACH ALGEBRAS
( Ali Ebadian ),( Fariba Farajpour ),( Shahram Najafzadeh ) 호남수학회 2021 호남수학학술지 Vol.43 No.1
This paper considers pseudo Jordan homomorphisms on module extensions of Banach algebras and triangular Banach algebras. We characterize pseudo Jordan homomorphisms on module extensions of Banach algebras and triangular Banach algebras. Moreover, we define pseudo derivations on the above stated Banach algebras and characterize this new notion on those algebras.
Generalized $(\theta, \phi)$-Derivations on Poisson Banach Algebras and Jordan Banach Algebras
Chun-Gil Park 충청수학회 2005 충청수학회지 Vol.18 No.2
In \cite{1}, the concept of generalized $(\theta, \phi)$-derivations on rings was introduced. In this paper, we introduce the concept of generalized $(\theta, \phi)$-derivations on Poisson Banach algebras and of generalized $(\theta, \phi)$-derivations on Jordan Banach algebras, and prove the Cauchy--Rassias stability of generalized $(\theta, \phi)$-derivations on Poisson Banach algebras and of generalized $(\theta, \phi)$-derivations on Jordan Banach algebras.
GENERALIZED (, )-DERIVATIONS ON POISSON BANACH ALGEBRAS AND JORDAN BANACH ALGEBRAS
Park, Chun-Gil 충청수학회 2005 충청수학회지 Vol.18 No.2
In [1], the concept of generalized (${\theta}$, ${\phi}$)-derivations on rings was introduced. In this paper, we introduce the concept of generalized (${\theta}$, ${\phi}$)-derivations on Poisson Banach algebras and of generalizd (${\theta}$, ${\phi}$)-derivations on Jordan Banach algebras, and prove the Cauchy-Rassias stability of generalized (${\theta}$, ${\phi}$)-derivations on Poisson Banach algebras and of generalized (${\theta}$, ${\phi}$)-derivations on Jordan Banach algebras.
FUNCTIONAL EQUATIONS IN BANACH MODULES AND APPROXIMATE ALGEBRA HOMOMORPHISMS IN BANACH ALGEBRAS
Boo, Deok-Hoon,Kenary, Hassan Azadi,Park, Choonkil The Kangwon-Kyungki Mathematical Society 2011 한국수학논문집 Vol.19 No.1
We prove the Hyers-Ulam stability of partitioned functional equations in Banach modules over a unital $C^*$-algebra. It is applied to show the stability of algebra homomorphisms in Banach algebras associated with partitioned functional equations in Banach algebras.
Asymptotic aspect of derivations in Banach algebras
Roh, Jaiok,Chang, Ick-Soon Springer International Publishing 2017 Journal of inequalities and applications Vol.2017 No.1
<P>We prove that every approximate linear left derivation on a semisimple Banach algebra is continuous. Also, we consider linear derivations on Banach algebras and we first study the conditions for a linear derivation on a Banach algebra. Then we examine the functional inequalities related to a linear derivation and their stability. We finally take central linear derivations with radical ranges on semiprime Banach algebras and a continuous linear generalized left derivation on a semisimple Banach algebra.</P>
JORDAN DERIVATIONS ON NONCOMMUTATIVE BANACH ALGEBRAS
PARK, KYOO-HONG,KIM, BYONG-DO,BYUN SANGHUN 서원대학교 기초과학연구소 2001 基礎科學硏究論叢 Vol.15 No.-
In this paper we shall give a slight generalization of J. Vukman's Theorem. And show from the result that the image of a continuous linear Jordan derivation on a noncommutative Banach algebra A is contained in the radical under the condition [D(χ), χ]E(χ) ∈ rad(A) for all χ ∈ A. And we show some properties of the derivationts on noncommutative Banach algebras. AMS Mathematics Subject Classification : 46H40.46J10,47B47 Key words and phrases : torsion free ring, derivation, Jordan derivation, prime ring, semisimple, noncommutative Banach algebra.
CYCLIC FUNCTIONAL EQUATIONS IN BANACH MODULES OVER A UNITAL $C^{*}$-ALGEBRA
Park, Chun-Gil 한국전산응용수학회 2004 Journal of applied mathematics & informatics Vol.15 No.1
We prove the generalized Hyers-Ulam-Rassias stability of cyclic functional equations in Banach modules over a unital $C^{*}$-algebra. It is applied to show the stability of algebra homomorphisms between Banach algebras associated with cyclic functional equations in Banach algebras.
WEIGHTED MOORE-PENROSE INVERTIBLE AND WEIGHTED EP BANACH ALGEBRA ELEMENTS
Boasso, Enrico,Djordjevic, Dragan S.,Mosic, Dijana Korean Mathematical Society 2013 대한수학회지 Vol.50 No.6
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.
GENERALIZED JENSEN'S FUNCTIONAL EQUATIONS AND APPROXIMATE ALGEBRA HOMOMORPHISMS
Bae, Jae-Hyeong,Park, Won-Gil Korean Mathematical Society 2002 대한수학회보 Vol.39 No.3
We prove the generalized Hyers-Ulam-Rassias stability of generalized Jensen's functional equations in Banach modules over a unital $C^{*}$-algebra. It is applied to show the stability of algebra homomorphisms between Banach algebras associated with generalized Jensen's functional equations in Banach algebras.
Weighted Moore-Penrose invertible and weighted EP Banach algebra elements
Enrico Boasso,Dragan S. Djordjevic,Dijana Mosić 대한수학회 2013 대한수학회지 Vol.50 No.6
The weighted Moore-Penrose inverse will be introduced and studied in thecontext of Banach algebras. In addition, weighted EP Banach algebra elements will be characterized. The Banach space operator case will be also considered.