Lightning Network: can I create a channel from a preexisting channel?

Lightning Network: can I create a channel from a preexisting channel?

If I open a channel with myself for 0.01 BTC, with one end having all, and the other having none, could I create an updated contract, or state, to send 0.001 BTC to an address owned by Alice, even though this address would not be in the blockchain, whereby she now has a valid channel with 0.001 BTC, and I have 0.009?

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