de la Harpe, Pierre; Skandalis, G. Déterminant associé à une trace sur une algèbre de Banach. (French) Zbl 0521.46037 Ann. Inst. Fourier 34, No. 1, 241-260 (1984). Page: −5 −4 −3 −2 −1 ±0 +1 +2 +3 +4 +5 Show Scanned Page Cited in 3 ReviewsCited in 43 Documents MSC: 46H05 General theory of topological algebras 46M20 Methods of algebraic topology in functional analysis (cohomology, sheaf and bundle theory, etc.) Keywords:determinant; Grothendieck group; Whitehead group; trace × Cite Format Result Cite Review PDF Full Text: DOI Numdam EuDML Link References: [1] [1] , An analogue of the Thom isomorphism for crossed products of a C*-algebra by an action of R, Adv. in Math., 39 (1981), 31-55. · Zbl 0461.46043 [2] [2] , The internal structure of simple C*-algebras, In Proc. Symp. Pure Math., 38, Amer. Math. Soc., 1981. · Zbl 0502.46039 [3] [3] et , Equivalence and traces on C*-algebras, J. Functional Analysis, 33 (1979), 135-164. · Zbl 0427.46042 [4] [4] et , Linear operators. Part II: Spectral theory, Interscience, 1963. · Zbl 0128.34803 [5] [5] , et , Dimension groups and their affine representations, Amer. J. Math., 102 (1980), 385-407. · Zbl 0457.46047 [6] [6] , On the classification of inductive limits of sequences of semi-simple finite-dimensional algebras, J. Algebra, 38 (1976), 29-44. · Zbl 0323.46063 [7] [7] , Finite sums of commutators in C*-algebras, Ann. Inst. Fourier, 32-1 (1982), 129-137. · Zbl 0464.46047 [8] [8] et , Determinant theory in finite factors, Ann. Math., 55 (1952), 520-530. · Zbl 0046.33604 [9] [9] , Un résultat sur le dual d’une C*-algèbre, Journal de Math., 36 (1957), 97-108. · Zbl 0083.10401 [10] [10] , communication non publiée. [11] [11] , K-theory, an introduction, Springer, 1978. · Zbl 0382.55002 [12] [12] , K-théorie algébrique de certaines algèbres d’opérateurs, Lecture Notes in Math., 725 (1979), 254-290. · Zbl 0444.46054 [13] [13] et , Ideals in a C*-algebra, Math. Scand., 27 (1970), 193-204. · Zbl 0218.46056 [14] [14] et , Imbedding the irrational rotation C*-algebra into an AF-algebra, J. Operator theory, 4 (1980), 201-210. · Zbl 0525.46031 [15] [15] , Banach algebras and topology in “Algebras in Analysis”, J.H. Williamson, ed., Academic Press, (1975) 118-186. · Zbl 0439.46053 [16] [16] , Groups of invertible elements of Banach algebras, Bull. Amer. Math. Soc., 79 (1973), 82-84. · Zbl 0252.46060 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.