Hostname: page-component-8448b6f56d-42gr6 Total loading time: 0 Render date: 2024-04-19T23:49:02.031Z Has data issue: false hasContentIssue false
  • English
  • Français

Linear equations in B(ℤ)*

Published online by Cambridge University Press:  14 November 2011

M. Filali
M. Filali
Affiliation:
Department of Mathematics, University of Oulu, 90570, Finland
Get access Rights & Permissions [Opens in a new window]

Synopsis

Let B(ℤ)* be the Banach dual of the space of all bounded complex-valued functions on ℤ. For each n ε ℤ, let Ln be the translation operator on B(ℤ) and Tn be its adjoint operator on B(ℤ)*. This paper concerns itself with equations of the form

where (an)nεℤ is a sequence of complex numbers.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 123 , Issue 6 , 1993 , pp. 1001 - 1009
Copyright
Copyright © Royal Society of Edinburgh 1993

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), 509–544.CrossRefGoogle Scholar
2Dunford, N. and Schwartz, J.. Linear Operators I (New York: Interscience, 1966).Google Scholar
3Filali, M.. The uniform compactification of a locally compact abelian group. Math. Proc. Cambridge Philos. Soc. 108 (1990), 527–538.Google Scholar
4Filali, M.. The ideal structure of some Banach algebras. Math. Proc. Cambridge Philos. Soc. 111 (1992), 567–576.CrossRefGoogle Scholar
5Hewitt, E. and Ross, K. A.. Abstract Harmonic Analysis I (Berlin: Springer, 1963).Google Scholar
6Hewitt, E. and Ross, K. A.. Abstract Harmonic Analysis II (Berlin: Springer, 1970).Google Scholar
7Hindman, N.. Minimal ideals and cancellation in βℕ. Semigroup Forum 25 (1982), 291–310.Google Scholar
8Parsons, D. J.. The centre of the second dual of a commutative semi-group algebra. Math. Proc. Cambridge Philos. Soc. 95 (1984), 71–92.Google Scholar
9Simmons, G. F.. Introduction to Topology and Modern Analysis (New York: McGraw–Hill, 1963).Google Scholar