اشتقاق‌ها روی جبرهای باناخ وابسته به رده خاصی از نیم‌گروه‌های توپولوژیکی

نوع مقاله : مقاله پژوهشی

نویسنده

دانشکده مهندسی، دانشکدگان فارابی، دانشگاه تهران، تهران، ایران

چکیده

در این مقاله به مطالعه اشتقاق‌ها روی جبر باناخ $L_0^{\infty}(S;M_a(S))^{\ast}$ برای رده خاصی از نیم‌گروه‌های توپولوژیک جابجایی 
$S$ می‌پردازیم. ما ثابت می‌کنیم که تصویر هر اشتقاق روی $L_0^{\infty}(S;M_a(S))^{\ast}$ در رادیکالش قرار دارد. همچنین اشتقاق روی $L_0^{\infty}(S;M_a(S))^{\ast}$ پیوسته است اگر و تنها اگر تحدید آن اشتقاق به پوچساز راست$L_0^{\infty}(S;M_a(S))^{\ast}$ 
پیوسته باشد. درنهایت یکی از یافته‌های اصلی این مقاله نتیجه می‌دهد که تنها اشتقاق مرکز ساز روی$L_0^{\infty}(S;M_a(S))^{\ast}$ 
نگاشت صفر است. 

کلیدواژه‌ها

موضوعات

عنوان مقاله [English]

Derivations on Banach algebras related to certain class of topological semigroup

نویسنده [English]

  • Ahmad Alinejad
Department of Engineering, College of Farabi, University of Tehran, Iran
چکیده [English]

In this paper, we investigate derivations on the Banach algebra $L_{0}^{\infty}(S;M_a(S))^*$ for certain class of topological semigroup. We show that any derivation on $L_{0}^{\infty}(S;M_a(S))^*$ maps it into its radical and a derivation on $L_{0}^{\infty}(S;M_a(S))^*$ is continuous if and only if its restriction to the right annihilator of $L_{0}^{\infty}(S;M_a(S))^*$ is continuous. Finally, we prove that the zero map is the only centralizing derivation on $L_{0}^{\infty}(S;M_a(S))^*$.

کلیدواژه‌ها [English]

  • Derivation
  • Foundation semigroup
  • Compactly cancellative semigroup
  • Semigroup algebra
  • Measure algebra

مراجع

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  • تاریخ دریافت: 11 مرداد 1403
  • تاریخ بازنگری: 03 آبان 1403
  • تاریخ پذیرش: 10 آبان 1403

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