IJPAM: Volume 81, No. 3 (2012)

A SCHUR-TYPE THEOREM FOR
${\mathcal I}$-CONVERGENCE AND MAXIMAL IDEALS

A. Boccuto$^1$, P. Das$^2$, X. Dimitriou$^3$
$^1$Department of Mathematics and Computer Sciences
University of Perugia
via Vanvitelli 1, I-06123 Perugia, ITALY
$^2$Department of Mathematics
Jadavpur University
Kolkata, 700032, West Bengal, INDIA
$^3$Department of Mathematics
University of Athens
Panepistimiopolis, Athens 15784, GREECE


Abstract. A Schur-type theorem in the setting of ideal convergence is proved. Some properties of ideal convergence in relation with usual convergence of suitable subsequences are investigated, and a characterization of maximal ideals is given. Furthermore some open problem is posed.

Received: September 15, 2012

AMS Subject Classification: 28A20, 28B15, 54A20

Key Words and Phrases: admissible ideal, maximal ideal, $P$-ideal, ideal convergence, Schur theorem

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Source: International Journal of Pure and Applied Mathematics
ISSN printed version: 1311-8080
ISSN on-line version: 1314-3395
Year: 2012
Volume: 81
Issue: 3