Hilbert space frames containing a Riesz basis and Banach spaces which have no subspace isomorphic to c0c_0

We prove that a Hilbert space frame \fti contains a Riesz basis if every subfamily \ftj , J \subseteq I , is a frame for its closed span. Secondly we give a new characterization of Banach spaces which do not have any subspace isomorphic to $c_0$. This result immediately leads to an improvement of a recent theorem of Holub concerning frames consisting of a Riesz basis plus finitely many elements

Weyl-Heisenberg frames for subspaces of L^2(R)

We give sufficient conditions for translates and modulates of a function g in L^2(R) to be a frame for its closed linear span. Even in the case where this family spans all of L^2(R), wou conditions are significantly weaker than the previous known conditions.Comment: 13 page

Liv Ullmann’s Handling of Religious Themes in Her Adaptation of Sigrid Undset’s The Wreath

ABSTRACT: In 1995 Liv Ullmann released Kristin Lavransdatter, a film adaptation of The Wreath, the first novel in Sigrid Undset’s trilogy Kristin Lavransdatter, a novelistic reconstruction of fourteenth-century psychology and religious culture published between 1920 and 1922. This work was crucial to Undset’s winning the Nobel Prize in 1928 “principally for her powerful descriptions of Northern life during the Middle Ages”; though its historical accuracy has been challenged, the affection with which this work is held by Norwegian readers endures. So Ullmann was taking on well-known text, which had been authored by a keen Catholic apologist, when she undertook her adaptation. Her version of the story—or rather versions, since three different cuts have been released—reduces the religious dimension of the original while increasing the focus on the psychological exploration of family tensions, whether between generations, between marriage partners, between siblings—or between friends. A comparison of the two works, preceded by a brief discussion of Undset’s religious writings, illuminates each

Accelerated ageing and renal dysfunction links lower socioeconomic status and dietary phosphate intake

Background: We have sought to explore the impact of dietary Pi intake on human age related health in the pSoBid cohort (n=666) to explain the disparity between health and deprivation status in this cohort. As hyperphosphataemia is a driver of accelerated ageing in rodent models of progeria we tested whether variation in Pi levels in man associate with measures of biological ageing and health. Results: We observed significant relationships between serum Pi levels and markers of biological age (telomere length (p=0.040) and DNA methylation content (p=0.028), gender and chronological age (p=0.032). When analyses were adjusted for socio-economic status and nutritional factors, associations were observed between accelerated biological ageing (telomere length, genomic methylation content) and dietary derived Pi levels among the most deprived males, directly related to the frequency of red meat consumption. Conclusions: Accelerated ageing is associated with high serum Pi levels and frequency of red meat consumption. Our data provide evidence for a mechanistic link between high intake of Pi and age-related morbidities tied to socio-economic status