How can I convert from an E11 socket to an E26 socket?
I'm pretty sure that no one makes such an adapter, it would be a risky proposition for a manufacturer for these reasons:


The mechanical stresses on the socket would be too great.  The adaptor would be too prone to breaking or to destroying the socket.  For an idea about why too much mass is not good for too small a socket, Pick up a full, 2-liter soda bottle only by the cap and try to hold it horizontally.
Many (but not all) E11 sockets are only rated for 50 watts or less.  The temptation to use a 60-watt, or larger bulb, in an E26 socket would be too great -- a big fire risk.


The largest E11 upsizing adapter I've seen is an E11 to E17.

The smart thing to do would be to replace the fixtures or continue to use only E11 bulbs.


But, if you really want to earn your spot on the Redneck Repairs Blog, you could use two adapters:  The E11 to E17 and then an E17 to E26 (NOT recommended).