Košir, Tomaž; Omladič, Matjaž; Radjavi, Heydar Maximal semigroups dominated by \(0-1\) matrices. (English) Zbl 0866.47046 Semigroup Forum 54, No. 2, 175-189 (1997). Summary: Maximal semigroups dominated by a 0-1 matrix of a certain type are determined. The 0-1 matrices that dominate maximal bounded and maximal commuting semigroups are given. Also semigroup modules over maximal semigroups dominated by a 0-1 matrix are discussed. MSC: 47H20 Semigroups of nonlinear operators Keywords:maximal semigroups dominated by a 0-1 matrix of a certain type; maximal commuting semigroups PDFBibTeX XMLCite \textit{T. Košir} et al., Semigroup Forum 54, No. 2, 175--189 (1997; Zbl 0866.47046) Full Text: DOI References: [1] C. Davis, H. Radjavi, and P. Rosenthal,On Operator Algebras and Invariant Subspaces, Can. J. Math., 21:1178–1181, 1969. · Zbl 0186.45301 · doi:10.4153/CJM-1969-129-9 [2] K. Davidson,Invariant Operator Ranges and Reflexive Algebras, J. Operator Theory, 7:101–107, 1982. · Zbl 0486.47007 [3] K. Davidson, Nest Algebras,Longman Scientific & Technical U.K., 1988. [4] K. H. Hofmann and P. S. Mostert, Elements of Compact Semigroups,Charles E. Merrill, Columbus, 1966. · Zbl 0161.01901 [5] N. Jacobson, Basic Algebra II,W.H. Freeman & Co., San Francisco, 1980. [6] J. Lindenstrauss and L. Tzafriri, Classical Banach Spaces I. Sequence Spaces,Springer-Verlag, 1977. · Zbl 0362.46013 [7] M. Omladič and H. Radjavi,Maximal Bounded Irreducible Semigroups, preprint. [8] H. H. Schäfer, Banach Lattices and Positive Operators,Springer-Verlag, 1974. [9] L. B. Shneperman,On Maximal Compact Semigroups of the Endomorphism Semigroup of an n-dimensional Complex Vector Space, Semigroup Forum,47 (1993), 196–208. · Zbl 0790.20081 · doi:10.1007/BF02573756 [10] D. A. Suprunenko, Matrix Groups,Transl. of Math. Monographs 45,AMS, 1976. · Zbl 0317.20028 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.