Hostname: page-component-78c5997874-94fs2 Total loading time: 0 Render date: 2024-11-10T17:38:10.295Z Has data issue: false hasContentIssue false
  • English
  • Français

CLASSES OF SEQUENTIALLY LIMITED OPERATORS

Part of: Special classes of linear operators Topological linear spaces and related structures

Published online by Cambridge University Press:  22 July 2015

JAN H. FOURIE  and
ELROY D. ZEEKOEI
JAN H. FOURIE
Affiliation:
Unit for Business Mathematics and Informatics, North-West University(NWU), Private Bag X6001, Potchefstroom 2520, South Africa e-mail: jan.fourie@nwu.ac.za; elroy.zeekoei@nwu.ac.za
ELROY D. ZEEKOEI
Affiliation:
Unit for Business Mathematics and Informatics, North-West University(NWU), Private Bag X6001, Potchefstroom 2520, South Africa e-mail: jan.fourie@nwu.ac.za; elroy.zeekoei@nwu.ac.za
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

The purpose of this paper is to present a brief discussion of both the normed space of operator p-summable sequences in a Banach space and the normed space of sequentially p-limited operators. The focus is on proving that the vector space of all operator p-summable sequences in a Banach space is a Banach space itself and that the class of sequentially p-limited operators is a Banach operator ideal with respect to a suitable ideal norm- and to discuss some other properties and multiplication results of related classes of operators. These results are shown to fit into a general discussion of operator [Y,p]-summable sequences and relevant operator ideals.

MSC classification

Primary: 47B10: Operators belonging to operator ideals (nuclear, $p$-summing, in the Schatten-von Neumann classes, etc.)
Secondary: 46A45: Sequence spaces (including Köthe sequence spaces)
Type
Research Article
Information
Glasgow Mathematical Journal , Volume 58 , Issue 3 , September 2016 , pp. 573 - 586
Copyright
Copyright © Glasgow Mathematical Journal Trust 2015 

References

REFERENCES

1. Albiac, F. and Kalton, N. J., Topics in Banach spaces, Graduate Texts in Mathematics (Springer Inc., USA, 2006).Google Scholar
2. Aywa, S. and Fourie, J. H., On convergence of sections of sequences in Banach spaces, Rendiconti del Circolo Matematico di Palermo, Serie II, XLIX (2000), 141–150.CrossRefGoogle Scholar
3. Conway, J. B., A course in Functional Analysis, Graduate Texts in Mathematics, 2nd Edition (Springer-Verlag, New York, Inc., 1990).Google Scholar
4. Diestel, J., Jarchow, H. and Tonge, A., Absolutely summing operators (Cambridge University Press, Cambridge, 1995).CrossRefGoogle Scholar
5. Fourie, J. H. and Swart, J., Banach ideals of p-compact operators, Manuscr. Math., 26 (4) (1979), 349–362.Google Scholar
6. Karn, A. K. and Sinha, D. P., An operator summability of sequences in Banach spaces, Glasgow Math. J. 56 (2) (2014), 427–437.Google Scholar
7. Pietsch, A., Operator ideals (North-Holland, North-Holland Publishing Company, Amsterdam, New York, Oxford. 1980).Google Scholar