**Unitary equivalence of weighted shifts**

Let H be a nonzero Hilbert space and **B**(H) be the algebra of bounded operators defined on H.

Let {S_{n}}_{n∈Z} ⊆ **B**(H) be a two-sided sequence of bounded nonzero operators such that {||S_n||}_{n∈Z} is bounded.

We say that an operator S:⊕_{n∈Z} H → ⊕_{n∈Z}H is a *bilateral operator valued weighted shift* defined on H if for all x∈⊕_{n∈Z} H it holds that

Sx = (…, S_{-1}x_{-2},S_{0}x_{-1}, S_{1}x_{0}, …),

where x = (…, x_{-1}, x_{0}, x_{1}, …) and x_{0} denotes the central element of x.

This talk is based on my recent work related to unitary equivalence of bilateral operator valued weighted shifts.