The tennis sweater is a spring & summer classic. Traditionally the tennis sweater is a white / cream v-neck cable knit sweater with a stripe or two around collar. This tennis sweater I am wearing in this photo, shockingly and oddly, has no stripes around the collar, as you can see. Some may not even consider this a true bonafide tennis sweater due to the absence of stripes. For them, this would just be considered a white / cream v-neck cable knit sweater. Linguistically, it doesn't really matter what one calls it. Just the other day I was discussing with a follower this exact fact - there are so many different names that so many different people and makers use that at this point, the words aren't so helpful in clear identification, you really have to see it for yourself.
I found this sweater at a thrift store some years back for $3.99. It is Eddie Bauer and in near perfect condition. To be honest, I was actually very excited particularly by the absence of stripes on this tennis sweater, or white / cream v-neck cable knit sweater if you prefer. The absence of stripes makes this a much more versatile sweater. If you add stripes you are no longer a neutral piece and the outfit possibilities shrink immediately. The tennis sweater look - deep v-neck with white / cream cable knit, yet without stripes making it a neutral versatile spring & summer sweater is, in my opinion, the best of all worlds. With this neutrality I can pair this sweater with pink, green, baby blue, navy or red chinos and practically any color shirt (with the exception of yellow) as well. I cannot recommend the tennis sweater (senza stripes) enough. They may be a bit harder to find, but if you come across one, I say "buy it!" I am almost certain you will not regret it.