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Solutions to some problems in amenable semigroups

  • S. K. Ayyaswamy (a1) and P. V. Ramakrishnan (a2)

Synopsis

This paper discusses a few problems on the size of the set of invariant means of an amenable semigroup posed by Maria M. Klawe, Alan L. T. Paterson and M. Rajagopalan and P. V. Ramakrishnan ([4], [5], [8] and [9]).

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1Day, M. M.. Amenable Semigroups. Illinois J. Math. 1 (1957), 509544.
2Granirer, E.. A Theorem on Amenable semigroups. Trans. Amer. Maths. Soc. 111 (1964), 367399.
3Granirer, E.. Extremely Amenable Semigroups I and II. Math. Scand. 17 (1965a), 177197; 20 (1967), 93–113.
4Klawe, Maria M.. On the dimension of left invariant means and left thick subsets. Trans. Amer. Math. Soc. 231 (1977), 507518.
5Maria, M. Klawe. Dimensions of the set of invariant means of semigroups, Illinois. J. Math. 24 (1980), 233243.
6Mitchell, T.. Constant functions and left invariant means on semi-groups. Trans. Amer. Math. Soc. 119 (1965), 244261.
7Paterson, Alan L. T.. The size of the set of left invariant means on an ELA semigroup. Proc. Amer. Math. Soc. 72 (1978), 6264.
8Paterson, Alan L. T.. The cardinality of the set of left invariant means on a left amenable semigroup. Illinois. J. Math. 29 (1985) (to appear).
9Rajagopalan, M. and Ramakrishnan, P. V.. Uses of ßS in invariant means and extremely left amenable semigroups. Contemporary Mathematics, Amer. Math. 32.

Solutions to some problems in amenable semigroups

  • S. K. Ayyaswamy (a1) and P. V. Ramakrishnan (a2)

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