Why is ozone a greenhouse gas if it absorb UV radiation? Ozone is considered a greenhouse gas, even though it absorbs shortwave (UV) radiation from the Sun, which does not fit with the definition for greenhouse gases, where they are supposed to:


  "absorbs and emits radiant energy within the thermal infrared range"


(Quote from Wikipedia)



PS: This is an adaptation of a question asked in the private discussion board of a first year university course on Earth Sciences, that I'm copying here so a wider community can benefit from it and the corresponding answer. As suggested by the moderators, I'll donate any reputation received from this question in the form of a bounty awarded to exceptional answers (in particular by new or low-rep users).
Ozone is indeed a greenhouse gas. But not due to its capacity to absorb/scatter UV radiation, but instead due to its capacity to absorb infrared radiation. In contrast with other greenhouse gases (Like $CO_2$ or Methane), the spectral absorption bands of Ozone are not confined to the infrared part of the spectrum, there are ozone absorption bands also the UV too.
However, if ozone were capable to absorb only UV radiation, it would NOT be a greenhouse gas. Because the Earth's surface do not emit UV radiation.

Therefore, the greenhouse gas properties of Ozone do not come from its ultraviolet absorption bands, but instead from its infrared absorption bands, that you can see in the following infrared spectrum obtained from NIST: