On the Functional Equation $\boldsymbol{U}_{\boldsymbol{t}}\boldsymbol{+} \boldsymbol{U}_{\boldsymbol{-t}} = \boldsymbol{V}_{\boldsymbol{t}} \boldsymbol{+} \boldsymbol{V}_{\boldsymbol{-t}}$ in a Banach Space
DOI:
https://doi.org/10.5644/SJM.03.2.10Keywords:
Commuting one-parameter group of unitary operators, reflexive strictly convex Banach space with Gateaux differentiable normAbstract
In this paper we consider commuting one-parameter groups, $\{U_{t} : t \in R\}$ and $\{V_{t} : t\in R\}$ of unitary operators and the functional equation $U_{t} + U_{-t} = V_{t} + V_{-t}$ on a reflexive strictly convex Banach space with Gateaux differentiable norm.
2000 Mathematics Subject Classification. 47D03
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