000			02067nam a22002417a 4500
003			ISI Library, Kolkata
005			20240614062836.0
008			240614b |||||||| |||| 00| 0 eng d
020			_a9782856299821
040			_aISI Library _bEnglish
082	0	4	_223 _a512.556 _bAS853
100	1		_aSukochev, Fedor _eauthor
245	1	0	_aThe Connes character formula for locally compact spectral triples/ _cFedor Sukochev & Dmitriy Zanin
260			_aMarseille: _bSociété Mathématique de France, _c2023
300			_avi, 152 pages; _c20 cm.
490			_aAstérisque _v445
504			_aIncludes bibliography
505	0		_aIntroduction -- Preliminaries -- Special triples: Basic properties and examples -- Asymptotic of the heat trace -- Residue of the ζ-function and the Connes character formula -- Appendix
520	3		_aA fundamental tool in noncommutative geometry is Connes's character formula. This formula is used in an essential way in the applications of noncommutative geometry to index theory and to the spectral characterization of manifolds. A non-compact space is modeled in noncommutative geometry by a non-unital spectral triple. The authors' aim is to establish Connes's character formula for non-unital spectral triples. This is significantly more difficult than in the unital case, and they achieve it with the use of recently developed double operator integration techniques. Previously, only partial extensions of Connes's character formula to the non-unital case were known. In the course of the proof, the authors establish two more results of importance in noncommutative geometry: an asymptotic for the heat semigroup of a non-unital spectral triple and the analyticity of the associated [Riemann zeta] function. The authors require certain assumptions on the underlying spectral triple and verify these assumptions in the case of spectral triples associated to arbitrary complete Riemannian manifolds and also in the case of Moyal planes.
650	0		_aOperator Algebras
700	1		_aZanin, Dmitriy _eauthor
942			_2ddc _cBK
999			_c433837 _d433837