The Quran states that the people of Jannah will greet each other with salam, and will (often) utter alhamdulliah. To my knowledge, there is no worship in Jannah. Is this explicitly mentioned in any hadith or implied in the Quran?
People of Jannah will do tasbeeh (Subhana Allah) and takbeer (Allahu Akbar) in their gratitude to Allah, and that is their worship.
The Prophet (SAW) said:
The inhabitants of Jannah will eat and drink therein, but they will not have to pass excrement, to blow their noses or to urinate. Their food will be digested producing belch which will give out a smell like that of musk. They will be inspired to declare the freedom of Allah from imperfection and proclaim His Greatness as easily as you breathe. (Sahih Muslim)
This hadith shows that there will be tasbeeh (glorification) and takbeer (declaration of greatness) but it will be as easy as breathing. Meaning, it will not take any effort.
This makes sense since Jannah is not a realm of work but of reward.