6 papers
On computing bound states of the Dirac and Schrödinger Equations
Gregory Beylkin, Joel Anderson, Robert J. Harrison
We cast the quantum chemistry problem of computing bound states as that of solving a set of auxiliary eigenvalue problems for a family of parameterized compact integral operators.…
Weak Paveability and the Kadison-Singer Problem
Charles A. Akemann, Joel Anderson, Betul Tanbay
The Kadison-Singer Problem (K-S) has expanded since 1959 to a very large number of equivalent problems in various fields. In the present paper we will introduce the notion of weak…
The Kadison-Singer problem for the direct sum of matrix algebras
Charles Akemann, Joel Anderson, Betul Tanbay
Let denote the algebra of complex matrices and write for the direct sum of the . So a typical element of has the form \[x = x_1\oplus x_2 \... \oplu…
The Spectral Scale and the k-Numerical Range
Charles A. Akemann, Joel Anderson
Suppose that c is a linear operator acting on an n-dimensional complex Hilbert Space H, and let tau denote the normalized trace on B(H). Set b_1 = (c+c*)/2 and b_2 = (c-c*)/2i, and…
A geometric spectral theory for n-tuples of self-adjoint operators in a finite von Neumann algebra: II
Charles A. Akemann, Joel Anderson
Given an n-tuple {b_1, ..., b_n} of self-adjoint operators in a finite von Neumann algebra M and a faithful, normal tracial state tau on M, we define a map Psi from M to R^{n+1} by…
Locally Minimal Projections
Charles A. Akemann, Joel Anderson
Given an n-tuple {a_1, ..., a_n} of self-adjoint operators on an infinite dimensional Hilbert space H and a positive integer k, there exists a projection p of rank k such that, for…