Changing a mathematical field once one has a tenure I have heard that, in mathematics, there might be several difficulties in changing one's field once one has a tenured position. I am wondering what those difficulties are. Is it possible at all?
Let me mention two difficulties I heard about.

Obviously, one has to learn a new area of math on a professional level, which is not easy.

These days, there is a strong pressure to get grants and, hence, to publish regularly. If one does not yet have a reputation of a serious expert in the new field it will be difficult to get a grant. This pressure is weaker if one has a tenure, but it still exists.
I found changing fields after tenure to be not much of a problem as a tenured mathematics professor.  The threat of losing some funding for a while is a serious issue if one has an expensive lab.  If one is doing theory, then grant funding is not so critical.  A sabbatical is a great time to study up on a new field.
I should add I am talking about moving to fields that have some connection with the old.  If there is no overlap in people or background theory, then this might be more challenging.
The greatest difficulty is the bruising of the ego.  The new field may not be open to your ideas, and you are essentially heading in as if you are a graduate student without an advisor to make the introductions.  You need to realize that it might be years before you get invited to the right conferences or get referees who really read your papers.
It can take a few years to really switch fields, but if one has tenure and a decent sabbatical program, it can be worth the effort.  One can keep some side projects in the old area to keep some papers coming in and to get excuses to meet your old friends at conferences at exotic locales (someday).  Coauthors are great for this.