What does $\operatorname{supp}(A)$ mean?

Question

I'm looking at a paper (specifically this one). In the paper, we have a positive operator $A$, and the operator $\operatorname{supp}(A)$ is supposed to be a projection operator.

Does anybody know what exactly $\operatorname{supp}$ is supposed to mean in this context? I suppose there must be a connection to the idea of the "support of a function", which would be a space. Perhaps $\operatorname{supp}(A)$ is meant to be the projection onto the orthogonal complement of the kernel.

In any case, I'm not sure what's meant here. Thanks for looking.

Answer 1

The paper is a bit short on explaining the notations that they perhaps consider to be common in the quantum world. The notations are available, for example, in this PhD thesis

• On page 51:

  Let $\overline{P}$ be the entry-wise complex conjugate of P.

• On page 55:

  With some abuse of notation, we identify a projector with the support of the space on which it projects. We denote the support of an operator $A$ by supp($A$).