Approximately Local Derivations | Zendy

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Approximately Local Derivations

Author(s) -

Samei Ebrahim

Publication year - 2005

Publication title -

journal of the london mathematical society

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 1.441

H-Index - 62

eISSN - 1469-7750

pISSN - 0024-6107

DOI - 10.1112/s0024610705006496

Subject(s) - banach algebra , mathematics , annihilator , bimodule , pure mathematics , bounded function , algebra over a field , banach space , mathematical analysis

Certain linear operators from a Banach algebra A into a Banach A ‐bimodule X , which are called approximately local derivations, are studied. It is shown that when A is a C * ‐algebra, a Banach algebra generated by idempotents, a semisimple annihilator Banach algebra, or the group algebra of a SIN or a totally disconnected group, bounded approximately local derivations from A into X are derivations. This, in particular, extends a result of B. E. Johnson that ‘local derivations on C * ‐algebras are derivations’ and provides an alternative proof of it.

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