On limits of $L_p$-norms of an integral operator

Abstract

Summary. A r ecu rr ence r e l ation fo r the computation of the L p -no r ms of an He r mitian F r edho l m integ r a l operato r is de r ived and an expression giving approximate l y the number of eigenva l ues which in abso l ute va l ue a r e equa l to the spect r a l r adius is dete r mined. Using the L p -no r ms fo r the app r oximation of the spectra l radius of this ope r ato r an a p r iori and an a p o ste r io r i bound fo r the error a r e obtained. Some prope r ties of the a poste r iori bound a r e discussed.