The Relationship between Two Involutive Semigroups S and ST Is Defined by a Left Multiplier T. (14th August 2014)

• Record Type: Journal Article
• Authors: Mohammadi, S. M.; Laali, J.
• Other Names: Djordjevic Dragan Academic Editor.
• Is Part Of: Journal of function spaces. Volume 2014(2014)
• Publication Date: 2014-08-14
• Subjects: Function spaces -- Periodicals; 515.7305
• DOI: 10.1155/2014/851237
• Languages: English
• ISSNs: 2314-8896

Abstract

Abstract : LetS be a semigroup with a left multiplier T onS . There exists a new semigroupS T, which depends onS and T, which has the same underlying space asS . We study the question of involutions onS T and a Banach algebraA T . We find a condition of T under whichS T and the second dualA T * * * * admit an involution. We will show thatA T isC * -algebra if and only ifT : A T → A is an isometry, under mild conditions. Also, A isC * -algebra if and only if so isA T, under other minor conditions.