Conjugations on Banach $$*$$-algebras

Abstract

The notion of conjugation is extended to Banach * -algebras. The aim of this paper is to characterize conjugations on the Banach algebra of all bounded linear operators on a complex Hilbert space, the algebra of J-symmetric operators on a complex Hilbert space with given conjugation J and the algebra of all complex valued continuous functions, defined on a connected locally compact Hausdorff space, which vanish at infinity.

Conjugations of unitary operators, II

“…By the polarization identity, a conjugation also satisfies Conjugations play an important role in operator theory and were initially studied in [ 8 , 9 , 11 – 13 ]. More recently, conjugations were explored in [ 3 , 4 , 6 , 7 , 18 , 21 ].…”

The square roots of some classical operators

“…Conjugations play an important role in operator theory and were initially studied in [13,14,17,18,19]. More recently, conjugations were explored in various settings and applications in [4,5,11,12,27,32].…”