6th Summer Workshop on Operator Theory

9th - 13th July 2018 Kraków

Jakub Kośmider

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 {Sn}n∈ZB(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∈ZH is a bilateral operator valued weighted shift defined on H if for all x∈⊕n∈Z H it holds that

Sx = (…, S-1x-2,S0x-1, S1x0, …),

where x = (…, x-1, x0, x1, …) and x0 denotes the central element of x.

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

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