Lefschetz Numbers and Geometry of Operators in W*-modules
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arXiv
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| Format: | Preprint |
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1995
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| _version_ | 1866913825730592768 |
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| author | Frank, Michael Troitsky, Evgenij V. |
| author_facet | Frank, Michael Troitsky, Evgenij V. |
| contents | 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 $K_0(A)ø\C$-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 $K_0(A)ø\C$.
(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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_funct_an_9501007 |
| institution | arXiv |
| publishDate | 1995 |
| record_format | arxiv |
| spellingShingle | Lefschetz Numbers and Geometry of Operators in W*-modules Frank, Michael Troitsky, Evgenij V. Functional Analysis Operator Algebras 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 $K_0(A)ø\C$-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 $K_0(A)ø\C$. (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. |
| title | Lefschetz Numbers and Geometry of Operators in W*-modules |
| topic | Functional Analysis Operator Algebras |
| url | https://arxiv.org/abs/funct-an/9501007 |