New York Journal of Mathematics
Volume 22 (2016) 265-275


Massoud Amini, Morteza Essmaili, and Mahmoud Filali

The second transpose of a derivation and weak amenability of the second dual Banach algebras

view    print

Published: March 11, 2016
Keywords: Derivation, second dual of Banach algebras, weak amenability
Subject: Primary 46H20, Secondary 47B47.

Let A be a Banach algebra, A*, A** and A*** be its first, second and third dual, respectively. Let R:A***A* be the restriction map, J: A*⟶A*** be the canonical injection and Λ: A***A*** be the composition of R and J. Let D:AA* be a continuous derivation and D'':A**A*** be its second transpose. We obtain a necessary and sufficient condition for Λ∘D'':A**⟶ (A**)* to be a derivation. We apply this to prove some results on weak amenability of second dual Banach algebras.


The first author was partly supported by a grant from IPM (No. 90430215).

Author information

Massoud Amini:
Department of Mathematics, Faculty of Mathematical Sciences, Tarbiat Modares University, 14115-134 Tehran, Iran and School of Mathematics, Institute for Research in Fundamental Sciences (IPM), P.O.Box 19395-5746, Tehran, Iran

Morteza Essmaili:
Department of Mathematics, Faculty of Mathematical and Computer Science, Kharazmi University, 50 Taleghani Avenue, 15618 Tehran, Iran

Mahmoud Filali:
Department of Mathematical Sciences, University of Oulu, P.O. Box 3000, Oulu 90014, Finland