Determination of a minimal projection from C [-1, 1] onto the quadratics

Section: Introductionmentioning

confidence: 89%

Codimension One Minimal Projections Onto the Quadratics

Prophet

1996

“…Mainly the problems concern existence (e.g., [7,10]), uniqueness (e.g., [6,9]), and formulas for minimal projections (e.g., [4,5,3]). For basic information concerning this topic, the reader is referred to [18].…”

Section: Introductionmentioning

confidence: 99%

A lower bound of the strongly unique minimal projection constant of l∞n, n⩾3

Odyniec

Prophet

2007

In this paper we give a lower bound for the strongly unique minimal projection (with norm one) constant (SUP-constant) onto some (n − k)-dimensional subspaces of l n ∞ (n 3, 1 k n − 1). By Proposition 1 of this paper, each k-dimensional Banach space with polytope unit ball with m (k − 1)-dimensional faces is isometrically isomorphic to a subspace of l k+m−1 ∞ . As such the aforementioned estimation can be applied to spaces other than l n ∞ . We also include a conjecture about the exact calculations of SUP-constants in particular settings.

“…That this problem is non-trivial is clear from the structure of the minimal projection from C[−1, 1] onto the quadratics (see [1] below):…”

mentioning

confidence: 97%

“…While Bruce's original idea did not work out, his tenacity kept our team of two working on the project for the next 20 years. Roughly eight years were spent on determining the form of the minimal projection (see [1] below), another eight years to develop a proof of minimality (see [2] below), and a final four years to get the results published.…”

mentioning

confidence: 99%

In Memoriam: Bruce L. Chalmers (1938–2015)

2016

and of Stanford University, Ph.D 1967. Bruce's dissertation was written under the direction of Stefan Bergman in the area of several complex variables, and was supported by an IBM fellowship. He joined the faculty of the Department of Mathematics at the University of California, Riverside, in the academic year 1967-68 beginning as Assistant Professor and rising in the ranks to Full Professor, until illness forced him into retirement at the end of the academic year 2007-08.After a few years of work related to Bergman's Kernel, Bruce has moved into Approximation Theory and Functional Analysis. Altogether he has written more than 70 papers in journals and refereed proceedings. He has the biggest number of papers in JAT by a non editor.Below is a collection of reminiscences of Bruce by colleagues and friends.