 The construction of Gelfand–Naimark "representation" depends only on the GNS construction and therefore it is meaningful for any Banach *-algebra "A" having an approximate identity.In general (when "A" is not a C*-algebra) it will not be a faithful representation.The closure of the image of π("A") will be a C*-algebra of operators called the C*-enveloping algebra of "A".