Lie∗Derivations and Lie Banach∗-algebra Homomorphisms Under the Hyers-Ulam Stability

سال انتشار: 1401
نوع سند: مقاله کنفرانسی
زبان: انگلیسی
مشاهده: 228

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شناسه ملی سند علمی:

MATHEMATICS10_019

تاریخ نمایه سازی: 24 خرداد 1401

چکیده مقاله:

Abstract. Let A be a Lie Banach∗-algebra. For each elements (a, b) and (c, d) in A۲ := A × A, by definitions (a, b)(c, d) = (ac, bd), ∥(a, b)∥ = ∥a∥ + ∥b∥, (a, b)∗ = (a∗, b∗), A۲ can be considered as a Banach∗-algebra. This Banach∗-algebra is called a Lie Banach∗-algebra whenever it is equipped with the following definitions of Lie product: [(a, b), (c, d)] =ac − ca ۲ , bd − db ۲ for all a, b, c, d in A. Also, if A is a Lie Banach∗-algebra, then D : A۲ −→ A۲ satisfying D([(a, b), (c, d)]) = [D(a, b), (c, d)] + [(a, b),D(c, d)] for all a, b, c, d ∈ A, is a Lie derivation on A۲. Furthermore, if A is a Lie Banach∗- algebra, then D is called a Lie∗ derivation on A۲ whenever D is a Lie derivation with D(a, b)∗ = D(a∗, b∗) for all a, b ∈ A. In this paper, we investigate the Hyers-Ulam stability of Lie Banach∗-algebra homomorphisms and Lie∗derivations on the Banach∗-algebra A۲.

نویسندگان

Javad Izadi

Department of Mathematics, Payame Noor University (PNU), Tehran, Iran.