Browder spectral systems

Abstract:

For two spectral systems ${\sigma _1}$ and ${\sigma _2}$ on a Banach space $\mathcal {X}$, the associated Browder spectral system is ${\sigma _{b;1,2}}: = {\sigma _1} \cup {\sigma ’_2}$. We prove that ${\sigma _{b;1,2}}$ possesses the projection and spectral mapping properties whenever ${\sigma _1}$ and ${\sigma _2}$ do (and satisfy a few additional mild assumptions). We also calculate ${\sigma _{b;1,2}}$ for tensor products. The results extend several previous works on Browder spectra.