Anti-Wick Symbols for Infinite Products in K-Homology |
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Authors: | Alexandr Kosyak and Richard Zekri |
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Institution: | (1) Ukrainian National Academy of Sciences, Institute of Mathématics, Tereshchinkivs'ka, 3, Kiev, 252601, Ukraine;(2) Faculté des sciences de Luminy, Institut de Mathématiques de Luminy, 163, Avenue de Luminy, 13288 Marseille Cedex 09, France |
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Abstract: | We consider infinite products in K-homology. We study these products in relation with operators on filtered Hilbert spaces, and infinite iterations of universal constructions on C*-algebras. In particular, infinite tensor power of extensions of pseudodifferential operators on R are considered. We extend anti-Wick pseudodifferential operators to infinite tensor products of spaces of the type L
2(R), and compare our infinite tensor power construction with an extension of pseudodifferential operators on R
. We show that the K-theory connecting maps coincide. We propose a natural definition of ellipticity for anti-Wick operators on R , compute the corresponding index, and draw some consequences concerning these operators. |
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Keywords: | K-homology index algebra of pseudodifferential operators infinite tensor product anti-Wick symbols |
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