Hostname: page-component-78c5997874-lj6df Total loading time: 0 Render date: 2024-11-09T16:12:19.222Z Has data issue: false hasContentIssue false

Solutions to some problems in amenable semigroups

Published online by Cambridge University Press:  14 November 2011

S. K. Ayyaswamy
Affiliation:
Arul Anandar College, Karuthmathur, Madurai-626 514, India
P. V. Ramakrishnan
Affiliation:
Department of Mathematics, Madurai Kamaraj University, Madurai-625 021, India

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]).

Type
Research Article
Copyright
Copyright © Royal Society of Edinburgh 1986

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

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