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A Dirac Type Operator on the Non-Commutative Disk

✍ Scribed by Alan L. Carey; Sławomir Klimek; Krzysztof P. Wojciechowski


Publisher
Springer
Year
2010
Tongue
English
Weight
184 KB
Volume
93
Category
Article
ISSN
0377-9017

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Given a commuting d-tuple T ¯=(T 1 , ..., T d ) of otherwise arbitrary operators on a Hilbert space, there is an associated Dirac operator D T ¯. Significant attributes of the d-tuple are best expressed in terms of D T ¯, including the Taylor spectrum and the notion of Fredholmness. In fact, all pro

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## By THOMAS FRIEDRICH of Berlin (Eingegangen am 9.9. 1980) Let M\* he a cony'act RIEMANNian spin inanifold with positive scalar curvature H and let R, denote its minimum. Consider the DIRAC operator D : r ( S ) + r ( S ) acting on sections of the associated spinor bundle S. If I.\* is the first p