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The role of matrices that are convergent to zero in the study of semilinear operator systems. (English) Zbl 1165.65336
Summary: We explain the advantage of vector-valued norms and the role of matrices that are convergent to zero in the study of semilinear operator systems by means of some basic methods of nonlinear analysis: the contraction principle, Schauder’s fixed point theorem, the Leray-Schauder continuation principle and Krasnoselskii’s cone fixed point theorem. A vector version of Krasnoselskii’s theorem is also established.

MSC:
65F30 Other matrix algorithms (MSC2010)
47J25 Iterative procedures involving nonlinear operators
15A99 Basic linear algebra
47H10 Fixed-point theorems
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