Is it permissible, in Sharia, to be bound by an obligation to purchase a partner's share at double the amount paid at the time of establishment, knowing that this obligation is binding upon me but not upon him?

There is no harm in your commitment to buy your partner's share, with his option to sell it to you, or to someone else, or not to sell it. However, setting a specific price for the share is considered a guarantee for the partner's capital or part of it, and this is not permissible in Sharia (definition). Rather, the selling price must be determined by the market value on the day of sale or by agreement at the time of sale, according to the resolution of the International Islamic Fiqh Academy.