LAUSR

Let E be a complex Banach space with open unit ball $$B_E.$$BE. For analytic self-maps $$\varphi $$φ of $$B_E$$BE with $$\varphi (0) =0,$$φ(0)=0, we investigate the spectra of weighted composition operators $$uC_\varphi $$uCφ acting on a large class of spaces of analytic functions. This class contains, for example, weighted Banach spaces of $$H^\infty $$H∞-type on $$B_E$$BE, weighted Bergman spaces $$A^p_\alpha ({\mathbb {B}}_N)$$Aαp(BN) and Hardy spaces $$H^p({\mathbb {B}}_N).$$Hp(BN). We present a general approach for deducing new information about the spectrum and for estimating the essential spectral radius of $$uC_\varphi .$$uCφ.