Norm attaining operators and pseudospectrum

It is shown that if $11$, the operator $I+T$ attains its norm. A reflexive Banach space $X$ and a bounded rank one operator $T$ on $X$ are constructed such that $\|I+T\|>1$ and $I+T$ does not attain its norm.

The level sets of the resolvent norm and convexity properties of Banach spaces

We construct a bounded linear operator on a separable, reflexive and strictly convex Banach space whose resolvent norm is constant in a neighbourhood of zero.

Negotiation of risk in sexual relationships and reproductive decision-making amongst HIV sero-different couples

The paper focuses on the ways in which medical discourses of HIV transmission risk, personal bodily meanings and reproductive decision-making are re-negotiated within the context of sero-different relationships, in which one partner is known to be HIV-positive. Eighteen in-depth interviews were conducted with 10 individuals in Northern Ireland during 2008–2009. Drawing on an embodied sociological approach, the findings show that physical pleasure, love, commitment, a desire to conceive without medical interventions and a dislike of condoms within regular ongoing relationships, shaped individuals' sense of biological risk. In addition, the subjective logic that a partner had not previously become infected through unprotected sex prior to knowledge of HIV status and the added security of an undetectable viral load significantly impacted upon women's and, especially, men's decisions to have unprotected sex in order to conceive. The findings speak to the importance of reframing public health campaigns and clinical counselling discourses on HIV risk transmission to acknowledge how couples negotiate this risk, alongside pleasure and commitment within ongoing relationships.