A weighted shift of multiplicity two with weight sequence {λn} is a bounded linear operator T on l² such that
T(x0, x1, x2, . . .) = (0, 0, λ0x0, λ1x1, λ2x2, . . .),
For all n ≥ 0 where λn ∈ C. The square root of T is a bounded operator Q such that Q² = T. It is known that the weighted shift of multiplicity one do not have any square root. This is not the case when we consider a weighted shift T of multiplicity two. In this talk, we present necessary and sufficient conditions on the weight sequence so that the set of square roots of T is non-empty. We show that when such conditions are satisfied, the set contains a certain special class of operators. We also present a complete description of all operators in the set of square roots of T.
Join us on Monday, Jan. 27, at 3:10 p.m. in Hayes 109 to hear this exciting presentation from Visiting Assistant Professor of Mathematics Tomas Miguel Rodriguez. We hope to see you there!