Abstract
An important problem in the theory of topological semigroups is to formulate a suitable definition of continuity for the choice of generalized inverses. In this paper, we will show that under certain natural conditions, a topology can be defined on a Rees matrix semigroup, which turns it into a topological semigroup, and in which a canonical continuous choice of inverses is possible. As an example, we show that this construction applied to the semigroup of operators of rank less than or equal to 1 on a Hilbert space gives a topology which is stronger than the norm topology, under which this semigroup is a topological semigroup and the assignment of every operator to its Moore-Penrose inverse is continuous.
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Krishnan, E., Sherly, V. (2015). Topological Rees Matrix Semigroups. In: Romeo, P., Meakin, J., Rajan, A. (eds) Semigroups, Algebras and Operator Theory. Springer Proceedings in Mathematics & Statistics, vol 142. Springer, New Delhi. https://doi.org/10.1007/978-81-322-2488-4_8
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DOI: https://doi.org/10.1007/978-81-322-2488-4_8
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