Estimating Norms of Commutators

We find estimates on the norms commutators of the form [f(x), y] in terms of the norm of [x, y] assuming that x and y are contractions in a C*-algebra A, with x normal and with spectrum within the domain of f. In particular we discuss [x^2, y] and [x^(1/2), y] for 0 <=, x <=, 1. For larger values of \delta = \|[x; y]\| we can rigorous calculate the best possible upper bound \|[f(x), y]\| for many f. In other cases we have conducted numerical experiments that strongly suggest that we have in many cases found the correct formula for the best upper bound.Comment: We are posting the next version of this paper at : http://repository.unm.edu/handle/1928/23462. Also posted at http://repository.unm.edu is theMatlab code used to generate example

How did the Sovereign debt crisis affect the Euro financial integration? A fractional cointegration approach.

This paper examines financial integration among stock markets in the Eurozone using the prices from each stock index. Monthly time series are constructed for four major stock indices for the period between 1998 and 2016. A fractional cointegrated vector autoregressive model is estimated at an international level. Our results show that there is a perfect and complete Euro financial integration. Considering the possible existence of structural breaks, this paper also examines the fractional cointegration within each regime, showing that Euro financial integration is very robust. However, in the financial and sovereign debt crisis regime, IBEX 35 appears to be the weak link in Euro financial integration, unless Euro financial integration recovers when this period ends