Spectral averaging for trace compatible operators

2007/04/13 by Nurulla Azamov, Azamov, Nurulla, Fyodor Sukochev +1
Mathematics · #47A11 #47A55 #FOS: Mathematics #Functional Analysis (math.FA) #Spectral Theory (math.SP) #math.FA #math.SP #msc:47A11 #msc:47A55

paper · pdf · doi:10.48550/arxiv.0704.1683

10 pages, LaTeX; a gap in the proof of Proposition 2.4 has been fixed

arxiv created 2007/05/25 · arxiv updated 2009/12/01

Abstract

In this note the notions of trace compatible operators and infinitesimal spectral flow are introduced. We define the spectral shift function as the integral of infinitesimal spectral flow. It is proved that the spectral shift function thus defined is absolutely continuous and Krein's formula is established. Some examples of trace compatible affine spaces of operators are given.

Related

• Some Applications of the Spectral Shift Operator
• The Spectral Shift Operator
• Absolute continuity of spectral shift
• Trace formulas in higher dimensions
• Functions of dissipative operators under relatively bounded and relatively trace class perturbations