ACC Seminar: The Numerical Index of a Banach Space

Abstract polygonal geometric surface

Department of Mathematical Sciences

Location: North Building, Room 103

Speaker: Monika, Stevens Institute of Technology

Abstract

The numerical index, n(X), of a Banach space X is a number relating the norm and the numerical range of a bounded linear operator. The problem of computing the numerical index of the  L_p spaces has been latent since the beginning of the theory. In this talk I will start with the basics of the numerical index and will show that

n(l^2_p) = sup_t∈[0,1] |t^(p−1) − t|/(1 + t^p)

for p ∈ [1.4547, 3.19925]. This result is an extension of the result by Javier Merı and Alicia Quero. Other recent results will also be discussed.

Refreshments at 3:30 pm

Virtual Option

Zoom: https://stevens.zoom.us/j/93228680142

Password: ACC