No.
I never use filters on any of my lenses unless there is a very particular reason for it. Long gone are the days when my serious film shooting required carrying around: about 60 different color correction and ND 4" Kodak gel filters, a dozen or so glass ones and a dozen or so plastic graduated filters of different color and density spreads, filter holders, thin guage black gaffer tape to work on lenses the filter holders didn't work with, my color temperatrure meter, self-made reciprocity failure and artificial lighting type correction charts custom made and researched for every individual film stock that specified filtering at various shutter speeds and lighting conditions. Good riddance! Now, things are a lot simpler and my use of filters massively curtailed.
For instance, in cases where atmospheric haze or high altitude is a factor, I will use a very specifically tuned UV filter (one of two B&W's that were ridiculously expensive), or if there is some environmental factor such as industrial grit or outdoor sand or rain/snow/sleet blowing towards the lens, I will use the mildest UV I own just to protect it.
Of course, I do use good quality polarizing filters when it would genuinely help an image or correct a problem with an image, as well as color correction, ND or graduated filters on the very rare occasions when changing camera settings or PP wouldn't work as well.
The days of always using a filter on the lens to "filter" every shot, due to a general inadequacy of the lens color response are long gone. Pretty much all modern photo lenses sufficiently filter UV on their own, and are color biased so that they also don't need the slightly pink filtering afforded by the ubiquitous "skylight" filter.
As for physical protection, some photographers who constantly work in situations where rough treatment might lead to physical scratches, or other similar damage to the front element, would be wise to keep a weak UV filter on the lens merely to "sacrifice" it in the event of disaster, instead of the front lens element. Neither my work, nor my pleasure shooting, fall into that category, so my 70-200, and all the others in my kit, are usually used "bare-as#ed-naked."
Regards,
David