Compressions of Resolvents and Maximal Radius of Regularity

Suppose that $\lambda - T$ is left-invertible in $L(H)$ for all $\lambda \in \Omega$, where $\Omega$ is an open subset of the complex plane. Then an operator-valued function $L(\lambda)$ is a left resolvent of $T$ in $\Omega$ if and only if $T$ has an extension $\tilde{T}$, the resolvent of which is a dilation of $L(\lambda)$ of a particular form. Generalized resolvents exist on every open set $U$, with $\bar{U}$ included in the regular domain of $T$. This implies a formula for the maximal radius of regularity of $T$ in terms of the spectral radius of its generalized inverses. A solution to an open problem raised by J. Zem\'anek is obtained.Comment: 15 pages, to appear in Trans. Amer. Math. So

National identification, endorsement of acculturation ideologies and prejudice: The impact of perceived threat of immigration

This paper examines how the perceived threat of immigration affects the links between national identification, endorsement of assimilation or multiculturalism, and prejudice against immigrants in France. One hundred thirty-five French undergraduates completed a questionnaire measuring these factors. Path analysis showed that higher national identification increased perception of immigrants as a threat, which in turn predicted increased endorsement of assimilation for immigrants. The link between endorsement of assimilation and prejudice was not significant. In contrast, lower national identification decreased perception of immigrants as a threat and, in turn, increased endorsement of multiculturalism and reduced levels of prejudice. An alternative model specifying perception of threat as an outcome of preferences for multiculturalism or assimilation did not fit the data well. Results suggest that perceived threat from immigration is the key factor that guides the preferences of the majority group for acculturation ideologies and, through these preferences, shapes intergroup attitudes

Escaping a neighborhood along a prescribed sequence in Lie groups and Banach algebras

It is shown that Jamison sequences, introduced in 2007 by Badea and Grivaux, arise naturally in the study of topological groups with no small subgroups, of Banach or normed algebra elements whose powers are close to identity along subsequences, and in characterizations of (self-adjoint) positive operators by the accretiveness of some of their powers. The common core of these results is a description of those sequences for which non-identity elements in Lie groups or normed algebras escape an arbitrary small neighborhood of the identity in a number of steps belonging to the given sequence. Several spectral characterizations of Jamison sequences are given, and other related results are proved