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Proceedings of the Estonian Academy of Sciences

ISSN 1736-7530 (electronic)   ISSN 1736-6046 (print)
Formerly: Proceedings of the Estonian Academy of Sciences, series Physics & Mathematics and  Chemistry
Published since 1952

Proceedings of the Estonian Academy of Sciences

ISSN 1736-7530 (electronic)   ISSN 1736-6046 (print)
Formerly: Proceedings of the Estonian Academy of Sciences, series Physics & Mathematics and  Chemistry
Published since 1952
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Representing the Banach operator ideal of completely continuous operators; pp. 189–193

(Full article in PDF format) https://doi.org/10.3176/proc.2017.2.10


Authors

Rauni Lillemets

Abstract

Let V ;W and W be the operator ideals of completely continuous, weakly -compact, and weakly compact operators, respectively. In a recent paper, William B. Johnson, Eve Oja, and the author proved that V = W ◦W -1 (Johnson, W. B., Lillemets, R., and Oja, E. Representing completely continuous operators through weakly -compact operators. Bull. London Math. Soc., 2016, 48, 452–456). We show that this equality also holds in the context of Banach operator ideals

Keywords

mathematics, Banach operator ideals, completely continuous operators, weakly compact operators, weakly ∞-compact operators.

References

1. Ain , K. , Lillemets , R. , and Oja , E. Compact operators which are defined by p-spaces. Quaest. Math. , 2012 , 35 , 145–159.
https://doi.org/10.2989/16073606.2012.696819

2. Ain , K. and Oja , E. On (p; r)-null sequences and their relatives. Math. Nachr. , 2015 , 288 , 1569–1580.
https://doi.org/10.1002/mana.201400300

3. Grothendieck , A. Produits tensoriels topologiques et espaces nucl´eaires. Mem. Am. Math. Soc. , 1955 , 16.

4. Lindenstrauss , J. and Tzafriri , L. Classical Banach Spaces I. Ergebnisse der Mathematik und ihrer Grenzgebiete 92. Springer–Verlag , Berlin–Heidelberg–New York , 1977.

5. Johnson , W. B. , Lillemets , R. , and Oja , E. Representing completely continuous operators through weakly-compact operators. Bull. London Math. Soc. , 2016 , 48 , 452–456.
https://doi.org/10.1112/blms/bdw015

6. Pietsch , A. Operator Ideals. Deutsch. Verlag Wiss. , Berlin , 1978; North-Holland Publishing Company , Amsterdam–New York–Oxford , 1980.

7. Sinha , D. P. and Karn , A. K. Compact operators whose adjoints factor through subspaces of ℓp. Studia Math. , 2002 , 150 , 17–33.
https://doi.org/10.4064/sm150-1-3

 

 
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Current Issue: Vol. 68, Issue 3, 2019




Publishing schedule:
No. 1: 20 March
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