This is a list of all upcoming talks for the next two weeks. Talks are from 3:45-4:45 p.m. in the Colloquium or Seminar Room, unless otherwise specified.
Oct 10Diagonality and Idempotents with Applications to Problems in Operator Theory and Frame Theory Prof. Gary Weiss University of Cincinnati Time: 03:45 PM Operator Algebras and Dynamics Seminars
View Abstract(Joint work with Jireh Loreaux.) We prove that a nonzero idempotent is zero-diagonal if and only if it is not a Hilbert-Schmidt perturbation of a projection, along with other useful equivalences. Zero-diagonal operators are those whose diagonal entries are identically zero in some basis. Our proof depends on work of Fan-Fong-Herrero on diagonals of operators. We also prove that any bounded sequence appears as the diagonal of some idempotent operator, thereby providing a characterization of inner products of dual frame pairs in infinite dimensions. Furthermore, we show that any absolutely summable sequence whose sum is a positive integer appears as the diagonal of a finite rank idempotent. We frame this work in a broader unifying context we call diagonality and explore historic and current work in this area. For instance, these characterizations extend to infinite dimensions the work of Giol, Kovalev, Larson, Nguyen and Tener on diagonals of idempotents.