Automatic Continuity of Some Types of Double Derivations on Semisimple Banach Algebras | Zendy

Amir A. Mohammed | Zendy; Lamia K. Ismail | Zendy

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Automatic Continuity of Some Types of Double Derivations on Semisimple Banach Algebras

Author(s) -

Amir A. Mohammed,

Lamia K. Ismail

Publication year - 2019

Publication title -

mağallaẗ al-tarbiyaẗ wa-al-ʻilm

Language(s) - English

Resource type - Journals

eISSN - 2664-2530

pISSN - 1812-125X

DOI - 10.33899/edusj.2019.160913

Subject(s) - mathematics , ideal (ethics) , pure mathematics , prime (order theory) , algebra over a field , type (biology) , combinatorics , law , political science , ecology , biology

Following Villena in [9] and Mohammed and Ali in [4], we introduce partially defined ( ) c double derivation and generalized ( ) c double derivation on a semisimple complex Banach algebra whose domain is not necessarily closed, essential ideal and we prove that they are closable. In particular, we show that every ( )c -double derivation and generalized ( ) c double derivation defined on any nonzero ideal of a prime C * algebra are continuous.

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