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Journal of Function Spaces
Volume 2014, Article ID 851237, 6 pages
Research Article

The Relationship between Two Involutive Semigroups and Is Defined by a Left Multiplier T

1Department of Mathematics Science and Research Branch, Islamic Azad University, Tehran, Iran
2Department of Mathematics, Faculty of Mathematical Science and Computer, Kharazmi University, 50 Taleghani Avenue, Tehran 15618, Iran

Received 8 April 2014; Revised 12 June 2014; Accepted 15 July 2014; Published 17 August 2014

Academic Editor: Dragan Djordjevic

Copyright © 2014 S. M. Mohammadi and J. Laali. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


Let be a semigroup with a left multiplier T on . There exists a new semigroup , which depends on and T, which has the same underlying space as . We study the question of involutions on and a Banach algebra . We find a condition of T under which and the second dual admit an involution. We will show that is -algebra if and only if is an isometry, under mild conditions. Also, is -algebra if and only if so is , under other minor conditions.