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This survey deals with the construction of a category of spectral triples that is compatible with the Kasparov product in $KK$-theory.
S.Baaj, Multiplicateurs non-bornés , Thesis, Université Pierre et Marie Curie, 1981
1981
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G.G. Kasparov, The operator K K -functor and extensions of C ∗ C^{*} -algebras , Izv. Akad. Nauk. SSSR Ser. Mat. 44(1980), 571-636; English transl., Math. USSR-Izv. 16 (1981), 513-572
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S.Baaj and P.Julg, Theorie bivariante de Kasparov et operateurs non-bornés dans les C ∗ C^{*} -modules hilbertiens , C.R.Acad.Sc.Paris 296 (1983), 875-878
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A.Connes, Noncommutative differential geometry , Publ. Math. IHES 62 (1986), 41-144
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J.Cuntz, A new look at K K KK -theory , K K -theory 1 (1987), 31-51
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N.Higson, Algebraic K K -theory of stable C ∗ C^{*} -algebras , Adv. in Math. 67 (1988) 1-140
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Z-J.Ruan, Subspaces of C ∗ C^{*} -algebras , J. Funct. Anal., 76 (1988), 217-230
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E.G Effros and Z.J.Ruan, On nonselfadjoint operator algebras , Proc. Amer.Math.Soc. vol 110 (4) (1990), 915-922
1990
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A.Connes, Noncommutative geometry , Academic press 1994
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A.Connes, Geometry from the spectral point of view , Lett. Math. Phys. 34 (1995), 203-238
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J. Cuntz and D. Quillen, Algebra extensions and nonsingularity , J.Amer. Math. Soc. , 8 , Amer. Math. Soc. (1995), 251-289
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E.C.Lance, Hilbert C ∗ C^{*} -modules , London Mathematical Society Lecture Note Series 210, Cambridge University Press 1995
D.P. Blecher, A generalization of Hilbert modules , J.Funct. An. 136, 365-421 (1996)
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D.P. Blecher, A new approach to Hilbert C ∗ C^{*} -modules , Math. Ann. 307, 253-290 (1997)
1997
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D. Kucerovsky, The K K KK -product of unbounded modules , K K -theory, 11(1997), 17-34
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D.P.Blecher, P.S.Muhly and V.I.Paulsen, Categories of Operator Modules , Memoirs of the AMS Vol.143 (2000), nr.681
2000
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N.Higson and J.Roe, Analytic K K -homology , Oxford Mathematical Monographs (2001)
2001
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A.Ya. Helemskii, Tensor products in quantum functional analysis: the non-coordinate approach , in: Topological algebras and applications , A.Mallios, M.Haralampidou (ed.), AMS Providence (2007), 199-224
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1995
Cited alongside, same era.
D.P.Blecher, Operator algebras and their modules , London Mathematical Society Monographs 30
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A.Carey, J.Philips, A.Rennie, Spectral triples and index theory, in Noncommutative Geometry and Physics: Renormalisation, Motives, Index Theory , ESI Lectures in Mathematics and Physics, 175-265
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A.Connes, On the spectral characterization of manifolds , arxiv 08102088
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B.Mesland, Unbounded bivariant K K -theory and correspondences in noncommutative geometry , to appear in J. Reine Angew. Math., arxiv 0904.4383
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2007
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