Lefschetz Numbers and Geometry of Operators in W*-modules

Details Lefschetz Numbers and Geometry of Operators in W*-modules Lefschetz Numbers and Geometry of Operators in W*-modules

1995-01-24

arxiv.org/abs/funct-an/9501007v1

Funct. Anal. Appl. 30(1996), no. 4, 257-266

Mathematics

Operator Algebras

LaTeX, 16 pages, preprint ZHS-NTZ February 1995, Univ. of Leipzig, Fed. Rep. Germany

Scientific paper

The main goal of the present paper is to generalize the results of~\cite{TroLNM,TroBoch} in the following way: To be able to define $K_0(A)\o\C$-valued Lefschetz numbers of the first type of an endomorphism $V$ on a C*-elliptic complex one usually assumes that $V=T_g$ for some representation $T_g$ of a compact group $G$ on the C*-elliptic complex. We try to refuse this restriction in the present paper. The price to pay for this is twofold: (i) $ $ We have to define Lefschetz numbers valued in some larger group as $K_0(A)\o\C$. (ii) We have to deal with W*-algebras instead of general unital C*-algebras. To obtain these results we have got a number of by-product facts on the theory of Hilbert W*- and C*-modules and on bounded module operators on them which are of independent interest.

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