On a generalisation of Krein's example

2017/10/30 by Post, Olaf, Uebersohn, Christoph
#35J25 #47A10 #47B35 #FOS: Mathematics #FOS: Physical sciences #Functional Analysis (math.FA) #Mathematical Physics (math-ph) #Primary 47B15 #Secondary 47A55 #Spectral Theory (math.SP)

paper · doi:10.48550/arxiv.1710.10975

Abstract

We generalise a classical example given by Krein in 1953. We compute the difference of the resolvents and the difference of the spectral projections explicitly. We further give a full description of the unitary invariants, i.e., of the spectrum and the multiplicity. Moreover, we observe a link between the difference of the spectral projections and Hankel operators.

Related

• On Krein's Example
• Invariant Krein subspaces, regular irreducibility and integral representations
• An Example of J-unitary Operator. Solving a Problem Stated by M.G. Krein
• The Krein spectral shift and rank one perturbations of spectra
• On the spectral Theory of Operator Measures