### 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
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# Representing the Banach operator ideal of completely continuous operators; pp. 189–193

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

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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

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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.

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 Current Issue: Vol. 68, Issue 3, 2019 Publishing schedule:No. 1: 20 MarchNo. 2: 20 JuneNo. 3: 20 SeptemberNo. 4: 20 December