In the paper under review the notion of middle point operator is introduced. The authors prove that for a givennonempty, bounded, $\rho$-closed, convex subset K of L1(μ), where $\rho$ is the metric of the convergencelocally in measure, if T from (K, $\rho$) to(K, $\rho$) is a continuous, $\rho$-nonexpansive, middle pointlinear operator, then T has at least one fixed point in K. To prove the theorem they use results ofA. V. Bukhvalov [in Operator theory in function spaces and Banach lattices, 95–112, Birkh¨auser,Basel, 1995; MR1322501 (95m:46123)] and M. Furi and A. Vignoli [Atti Accad. Naz. LinceiRend. Cl. Sci. Fis. Mat. Natur. (8) 48 (1970), 195–198; MR0279792 (43 #5513)]. Then they derivea Markov-Kakutani type fixed point theorem for commuting family of $\rho$-nonexpansive andmiddle point linear operators in L1(μ).
|Stato di pubblicazione||Published - 2009|