Furi–Martelli–Vignoli spectrum and Feng spectrum of nonlinear block operator matrices* *Project supported by the National Natural Science Foundation of China (Grant Nos. 11561048 and 11761029) and the Natural Science Foundation of Inner Mongolia, China (Grant Nos. 2019MS01019 and 2020ZD01).

Abstract

We investigate the Furi–Martelli–Vignoli spectrum and the Feng spectrum of continuous nonlinear block operator matrices, and mainly describe the relationship between the Furi–Martelli–Vignoli spectrum (compared to the Feng spectrum) of the whole operator matrix and that of its entries. In addition, the connection between the Furi–Martelli–Vignoli spectrum of the whole operator matrix and that of its Schur complement is presented by means of Schur decomposition.