Denseness for norm attaining operator-valued functions
Abstract In this note we offer a short, constructive proof for Hilbert spaces of Lindenstrauss' famous result on the denseness of norm attaining operators. Specifically, we show given any A∈ L ( H ) there is a sequence of rank-1 operators K n such that A+K n is norm attaining for each n and K n converges in norm to zero. We then apply our construction to establish denseness results for norm attaining operator-valued functions.
Denseness of norm-attaining operators into strictly convex spaces
We show that no infinite-dimensional Banach space provided with a strictly convex norm satisfies Lindenstrauss's property B. This is a generalization of previous results by Lindenstrauss for rotund spaces isomorphic to C0 and by Gowers for ℓp (1 < p < ∞). Also, there is an appropriate complex version of the announced result that works for all the C-strictly convex spaces. As a consequence, the Hardy space H1, any infinite-dimensional complex L1(μ), and, in general, any infinite-dimensional predual of a von Neumann algebra lacks Lindenstrauss's property B.
The denial of death and the out-of-the-body experience
The out-of-the-body experience is a phenomenon which continues to be reported and continues to be interpreted in many ways. It seems, however, that more attention is given to finding a spiritual base for this occurrence than a psychological understanding of it. This paper considers the psychological forces of denial as a suitable explanation for the OBE and suggests that these experiences may be understood as hallucinations caused by traumatic events rather than genuine previews of the afterlife. That is: “Do these people transcend their bodies and also time and space to acquire these experiences, or could it be that nothing has been transcended at all save the need to deny death and thus transcend its feared consequence, which is ‘not being’?”