It may seem obvious but leaving the team to just work is one of the key issues here. Different types of jobs demand different approach, and more often than not, the amount of work that can be done in a day will depend highly on the daily work plan.
If the team's job is actually in making things (manufacturing, writing, programming, graphic or other design etc.) the most significant disturbance to their workflow will be meetings.
It is crucial then to either eliminate them completely, or bulk them into a compressed time-span of a half to 1 day a week of meetings and 4 days of actual "work" work. So, limit the time required to be spent on not working and eliminate the harmful "wasted" time which results from having to prepare for and await a meeting. This way, your team can get into their work completely and get a lot more done in less time.
That said, everyone still needs regular breaks.
We are humans. This means, that however professional and self-controlled or not, ours and other people's emotions do have an impact on what and how we do.
So, if a manager takes no care of what emotions and for what reasons are being displayed and radiated to the team, teamwork results may bring no satisfaction. The role of a team manager is to lead, correct and facilitate. The emotions brought in with the management actions make a huge impact.
For instance, anger expressed after a project gone bad will be remembered by the team and will certainly make difference to the way the team acts during the next project. And it does not necessarily mean they will try harder.
Not meaning to say no emotions should be part of the management process, but knowing which of them will improve the situation at what point is crucial.
The Difficult People
All teams have some. It's the guy who always buries your idea out of the need to be the top dog at all times, or that irritating girl who annoys you with her personality alone to an extend, where you just don't even hear what she has to say. Or the pessimist who always assumes nothing will get done on time and comes up with reasons for why it won't, rather then with ways of making it work.
It can be a good idea to just avoid direct confrontation with these and similarly annoying kinds of people. Keep them at a distance - stick to email exchange, messenger communication or a task management tool which makes room for comments to each issue.
By keeping them away, you will get to focus on the merit of the communication, rather then personality or approach. Get the data and process it with no imprint of their spin on it.
That way, by respecting their personal qualities (keeping them away) you get the benefit of their actual work. Seems like a win-win situation.
Oh, and worry not — there is always someone who will see you as the difficult one, who needs to be managed. That's just the way it is.
The Space and Time
Because we are all different, it's hardly ever the case that an entire team will be comfortable and happy keeping the same office type, room or working hours.
This is why it makes sense to keep some of the office space adjustable — different kinds of seating arrangements, sofas, standing desks, etc.
Moreover, some of the modern approach companies allow for the team to set their own working hours. Keeping in mind that there is some overlap in the working time of the team members that do need to see each other — why wouldn't this be a good idea for the early birds to come in at dawn and to let the sleep-in types to come in at lunch time?
Provided that all in the team are able to reach their maximum productivity, the overall teamwork and final product should benefit.
Surely, there are plenty more factors when it comes to team productivity, but if you get the above 4 checked to a sensible level, your team's chances of succeeding will grow.