GENERALIZED σ-DERIVATION ON BANACH ALGEBRAS

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HOSSEINI A.; HASSANI M.; NIKNAM A.

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ISSN: 2588-4824

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Journal: BULLETIN OF THE IRANIAN MATHEMATICAL SOCIETY Year:2011 | Volume:37 | Issue:4 Page(s): 81-94

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Title

GENERALIZED σ-DERIVATION ON BANACH ALGEBRAS

Author(s)

HOSSEINI A. | HASSANI M. | NIKNAM A. | Issue Writer Certificate

Keywords

DERIVATION

σ-DERIVATION

(σ

D)-DERIVATION

σ-ALGEBRAIC MAP

Abstract

Let A be a Banach algebra and M be a Banach A-bimodule. We say that a linear mapping d: A®M is a generalized s-DERIVATION whenever there exists a s-DERIVATION d: A ® M such that d(ab) =d(a) s(b) +s(a)d(b), for all a, bÎ A. Giving some facts concerning generalized s-DERIVATIONs, we prove that if A is unital and if d: A®A is a generalized s-DERIVATION and there exists an elementa 2 A such that d (a) is invertible, then d is continuous if and only if d is continuous. We also show that if M is unital, has no zero divisor and d: A® M is a generalized s-DERIVATION such that d(1) ¹0, then ker (d) is a bi-ideal of A and ker(d) =ker (s) =ker (d), where 1 denotes the unit element of A.

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APA: Copy

HOSSEINI, A., HASSANI, M., & NIKNAM, A.. (2011). GENERALIZED σ-DERIVATION ON BANACH ALGEBRAS. BULLETIN OF THE IRANIAN MATHEMATICAL SOCIETY, 37(4), 81-94. SID. https://sid.ir/paper/582623/en

Vancouver: Copy

HOSSEINI A., HASSANI M., NIKNAM A.. GENERALIZED σ-DERIVATION ON BANACH ALGEBRAS. BULLETIN OF THE IRANIAN MATHEMATICAL SOCIETY[Internet]. 2011;37(4):81-94. Available from: https://sid.ir/paper/582623/en

IEEE: Copy

A. HOSSEINI, M. HASSANI, and A. NIKNAM, “GENERALIZED σ-DERIVATION ON BANACH ALGEBRAS,” BULLETIN OF THE IRANIAN MATHEMATICAL SOCIETY, vol. 37, no. 4, pp. 81–94, 2011, [Online]. Available: https://sid.ir/paper/582623/en

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