On commutativity of semiprime Banach algebras | Zendy

Arif Raza | Zendy; Nadeem ur Rehman | Zendy

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On commutativity of semiprime Banach algebras

Author(s) -

Arif Raza,

Nadeem ur Rehman

Publication year - 2018

Publication title -

acta et commentationes universitatis tartuensis de mathematica

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.276

H-Index - 6

eISSN - 2228-4699

pISSN - 1406-2283

DOI - 10.12697/acutm.2018.22.10

Subject(s) - commutative property , semiprime , pure mathematics , semiprime ring , mathematics , combinatorics , prime (order theory)

In the present paper, we discuss the commutativity of semi prime rings. Further, using this result, we establish that if U is a semiprime Banach algebra, and H-1 and H-2 are nonvoid open subsets of U which admit a continuous derivation d : U -> U such that d(x(m)) o d(y(n)) +/- x(m) o y(n) = 0 for all x is an element of H-1 and y is an element of H-2, where m,n are no longer fixed but they depend on the pair of elements x and y, then U is commutative.

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