It is, indeed, a side effect of owning cats.  That said, you can reduce the
problem (and help your cat avoid hairballs) by brushing regularly.  Try
different types of brushes -- some are much more effective at removing loose
fur, and some seem to actually exacerbate the problem you described.  My
favorite is the Zoom Groom brush by Kong (comes in a variety of
configurations -- just be sure to get one for cats and not one made for
dogs).  It gets an incredible amount of fur, and both of my cats love it.
Air filters may help to extract fur from the air, but they won't have any
effect on your cat.

MaryL

Photos of Duffy and Holly:      >'o'<
Duffy:  http://tinyurl.com/cslwf
Holly:  http://tinyurl.com/9t68o
Duffy and Holly together:  http://tinyurl.com/8b47e
Recent pics:  http://tinyurl.com/clal7

Shedding is definitely a side effect of owning cats, but since I started
adding Omega 3 oils to my cats diet, the situation has improved
dramatically. Perhaps this might be worthwhile investigating?