Displaying similar documents to “Multipliers and Wiener-Hopf operators on weighted L p spaces”

Bounds for the spectral radius of positive operators

Roman Drnovšek (2000)

Commentationes Mathematicae Universitatis Carolinae

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Let f be a non-zero positive vector of a Banach lattice L , and let T be a positive linear operator on L with the spectral radius r ( T ) . We find some groups of assumptions on L , T and f under which the inequalities sup { c ≥ 0 : T f ≥ c f } ≤ r ( T ) ≤ inf { c ≥ 0 : T f ≤ c f } hold. An application of our results gives simple upper and lower bounds for the spectral radius of a product of positive operators in terms of positive eigenvectors corresponding to the spectral radii of given operators. We thus extend the matrix result obtained by Johnson and...