Norms of positive operators on $L^ p$-spaces

Abstract:

Let $0 \leq T:{L^p}(Y,\nu ) \to {L^q}(X,\mu )$ be a positive linear operator and let $||T|{|_{p,q}}$ denote its operator norm. In this paper a method is given to compute $||T|{|_{p,q}}$ exactly or to bound $||T|{|_{p,q}}$ from above. As an application the exact norm $||V|{|_{p,q}}$ of the Volterra operator $Vf(x) = \int _0^x {f(t)dt}$ is computed.