The linear span of projections in AH algebras and for inclusions of C*-algebras

A $C^*$-algebra is said to have the LP property if the linear span of projections is dense in a given algebra. In the first part of this paper, we show that an AH algebra $A = \underrightarrow{\lim}(A_i,\phi_i)$ has the LP property if and only if every real-valued continuous function on the spectrum of $A_i$ (as an element of $A_i$ via the non-unital embedding) belongs to the closure of the linear span of projections in $A$. As a consequence, a diagonal AH-algebra has the LP property if it has small eigenvalue variation. The second contribution of this paper is that for an inclusion of unital $C^*$-algebras $P \subset A$ with a finite Watatani Index, if a faithful conditional expectation $E\colon A \rightarrow P$ has the Rokhlin property in the sense of Osaka and Teruya, then $P$ has the LP property under the condition $A$ has the LP property. As an application, let $A$ be a simple unital $C^*$-algebra with the LP property, $G$ a finite group and $\alpha$ an action of $G$ onto $\mathrm{Aut}(A)$. If $\alpha$ has the Rokhlin property in the sense of Izumi, then the fixed point algebra $A^G$ and the crossed product algebra $A \rtimes_\alpha G$ have the LP property. We also point out that there is a symmetry on CAR algebra, which is constructed by Elliott, such that its fixed point algebra does not have the LP property.Comment: 24 page

Theological medical ethics: A virtue based approach

Thesis advisor: LISA S. CAHILLThe Nuremberg trials ushered in a new era in which the four principles approach has become progressively the norm in Euro-American biomedical ethics, while the concepts of virtue and character become marginalized. In recent decades, the AIDS pandemic has highlighted the social aspects of health and illness, and the individualistic nature of the four principles approach proves inadequate in addressing the social causes of illness and poor health. At the global level, the promotion of the four principles approach as the universal norm can lead to the displacement of local values and customs, and the alienation of people from their cultural heritage. In this dissertation, I argue that although principles are indispensable, the virtue-based approach is more adequate in addressing these needs. The dissertation demonstrates that a virtue-based medical ethics informed by the gospel vision of healing would support models of health care that take seriously the social determinants of illness, and advocate action on behalf of the poor and the marginalized. At the global level, virtue-based medical ethics also allows the coexistence of the universal values and the local norms, and encourages cross-cultural dialogue. This dissertation develops a virtue-based medical ethics grounded in the Aristotelian teleological structure, and integrating insights obtained from the historical critical study of the healing narratives in Luke-Acts. It also provides a correlative study of the love command in Luke and the virtue of humaneness in the medical ethics of eighteenth century Vietnamese physician Hai Thuong Lan Ong. The concluding chapter brings these elements together in a discussion of the work of the Vietnamese Catholic AIDS care network.Thesis (PhD) — Boston College, 2013.Submitted to: Boston College. Graduate School of Arts and Sciences.Discipline: Theology