NDLI: Approximately n-Multiplicative Functionals on Banach Algebras

Content Provider	Springer Nature Link
Author	Shayanpour, H. Zohri, A. Heidarpour, Z. Ansari Piri, E.
Copyright Year	2015
Abstract	Let A be a normed algebra, $${\varphi:A\rightarrow \mathbb{C}}$$ be a linear functional. Then, the functional $${{(\varphi,n)}^{\vee}}$$ is defined as $${{(\varphi,n)}^{\vee}(a_{1},\dots, a_{n})=\varphi(a_{1} \dots a_{n})-\varphi(a_{1})\dots\varphi(a_{n})}$$ for all elements $${a_{1},\dots ,a_{n} \in A}$$ . If the norm of $${{(\varphi,n)}^{\vee}}$$ is small, then φ is approximately n-multiplicative linear functional and it is of interest whether or not $${\\|{(\varphi,n)}^{\vee}\\|}$$ being small implies that φ is near to an n-multiplicative linear functional. If this property holds for a Banach algebra A, then A is an n-AMNM algebra (approximately n-multiplicative linear functionals are near n-multiplicative linear functionals). We show that some properties of AMNM (2-AMNM) algebras are also valid for n-AMNM algebras. For example, we give some alternative definitions of n-AMNM. We also prove some theorems on the hereditary properties of n-AMNM condition and we use an equivalent condition for the n-AMNM property on certain Banach algebras when the Gelfand and norm topologies coincide on the character space of the algebra. We also give some examples which are n-AMNM and finally, exhibit an example which is not n-AMNM.
Ending Page	1920
Page Count	14
Starting Page	1907
File Format	PDF
ISSN	16605446
e-ISSN	16605454
Journal	Mediterranean Journal of Mathematics
Issue Number	4
Volume Number	13
Language	English
Publisher	Springer International Publishing
Publisher Date	2015-05-15
Publisher Place	Cham
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Banach algebra n-AMNM property Systems of functional equations and inequalities $${(\varepsilon, n)}$$ -multiplicative linear functional Approximately n-multiplicative linear functional Mathematics
Content Type	Text
Resource Type	Article
Subject	Mathematics

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