2007/12/13 by Ahmadreza Azimifard, Azimifard, Ahmadreza
Mathematics · #Advanced Operator Algebra Research #Advanced Banach Space Theory #Advanced Topics in Algebra
paper · pdf · doi:10.48550/arxiv.0712.2072
Associated to a nonzero homomorphism φ of a Banach algebra A, we regard special functionals, say mφ, on certain subspaces of A^∗ which provide equivalent statements to the existence of a bounded right approximate identity in the corresponding maximal ideal in A. For instance, applying a fixed point theorem yields an equivalent statement to the existence of a mφ on A^∗; and, in addition we expatiate the case that if a functional mφ is unique, then mφ belongs to the topological center of the bidual algebra A∗∗. An example of a function algebra, surprisingly, contradicts a conjecture that a Banach algebra A is amenable if A is φ-amenable in every character φ and if functionals mφ associated to the characters φ are uniformly bounded. Aforementioned are also elaborated on the direct sum of two given Banach algebras.