Phillips, N. Christopher The rectifiable metric on the space of projections in a \(C^*\)-algebra. (English) Zbl 0778.46039 Int. J. Math. 3, No. 5, 679-698 (1992). In analogy to the concept of exponential length introduced by J. Ringrose [Proc. R. Soc. Edinb., Sect. A 121, No. 1/2, 55-71 (1922; review below)], the notion of projective length of a \(C^*\)-algebra \(A\) is defined to be the supremum over the rectifiable distances, in the space of projections of \(A\), of any two projections in the same path component. For a unital \(C^*\)-algebra one finds that projective length \(\leq\) exponential length. There is also a closely related notion of projective rank. The paper contains computations and estimates of the projective length and rank for several examples of \(C^*\)-algebras. The case of Banach algebras is also discussed briefly. Reviewer: J.Cuntz (Heidelberg) Cited in 1 ReviewCited in 6 Documents MSC: 46L05 General theory of \(C^*\)-algebras Keywords:exponential length; projective length of a \(C^*\)-algebra; rank PDFBibTeX XMLCite \textit{N. C. Phillips}, Int. J. Math. 3, No. 5, 679--698 (1992; Zbl 0778.46039) Full Text: DOI