Static spectra and static families of Fredholm-type operators under tensor product

In this study, we introduce the static spectrum, the Weyl static families, the upper semi-Fredholm static families, and the Browder static families. These families consist of bounded linear operators parameterized by a scalar variable. We compare them, deriving conditions under which they form a Weyl static family. Finally, the tensor product of two families is introduced and studied to derive conditions guaranteeing that the tensor product forms a Browder static family or an upper semi-Fredholm static family.