ESTONIAN ACADEMY
PUBLISHERS
eesti teaduste
akadeemia kirjastus
cover
Proceedings of the Estonian Academy of Sciences. Physics. Mathematics
On interpolation of the measure of noncompactness; pp. 159–163
PDF | https://doi.org/10.3176/phys.math.2006.3.05

Authors
Fernando Cobos, Luz M. Fernández-Cabrera, Antón Martínez
Abstract

We revised the known results on interpolation of the measure of noncompactness and we announce a new approach to establishing the interpolation formula for the real method.

References

1. Bergh, J. and Löfström, J. Interpolation Spaces. An Introduction. Springer, Berlin, 1976. 
https://doi.org/10.1007/978-3-642-66451-9

2. Triebel, H. Interpolation Theory, Function Spaces, Differential Operators. North-Holland, Amsterdam, 1978. 

3. Cobos, F., Manzano, A. and Martínez, A. Interpolation theory and measures related to operator ideals. Quart. J. Math., 1999, 50, 401–416. 
https://doi.org/10.1093/qjmath/50.200.401

4. Cobos, F. and Martínez, A. Remarks on interpolation properties of the measure of weak non-compactness and ideal variations. Math. Nachr., 1999, 208, 93–100. 
https://doi.org/10.1002/mana.3212080104

5. Cobos, F., Fernández-Martínez, P. and Martínez, A. Interpolation of the measure of non- compactness by the real method. Studia Math., 1999, 135, 25–38. 

6. Schechter, M. Principles of Functional Analysis. American Mathematical Society, Providence, 2002. 
https://doi.org/10.1090/gsm/036

7. Cobos, F., Edmunds, D. E. and Potter, A. J. B. Real interpolation and compact linear operators. J. Funct. Anal., 1990, 88, 397–401. 
https://doi.org/10.1016/0022-1236(90)90110-7

8. Cobos, F. and Fernandez, D. L. On interpolation of compact operators. Ark. Mat., 1989, 27, 211–217. 
https://doi.org/10.1007/BF02386372

9. Cobos, F. and Peetre, J. Interpolation of compactness using Aronszajn–Gagliardo functors. Israel J. Math., 1989, 68, 220–240. 
https://doi.org/10.1007/BF02772662

10. Cobos, F., Kühn, T. and Schonbek, T. One-sided compactness results for Aronszajn– Gagliardo functors. J. Funct. Anal., 1992, 106, 274–313. 
https://doi.org/10.1016/0022-1236(92)90049-O

11. Teixeira, M. F. and Edmunds, D. E. Interpolation theory and measure of non-compactness. Math. Nachr., 1981, 104, 129–135. 
https://doi.org/10.1002/mana.19811040110

12. Cobos, F., Fernández-Cabrera, L. M. and Martínez, A. Abstract K and J spaces and measure of non-compactness. Math. Nachr. (to appear). 

13. Nilsson, P. Reiteration theorems for real interpolation and approximation spaces. Ann. Mat. Pura Appl., 1982, 132, 291–330. 
https://doi.org/10.1007/BF01760986

Back to Issue

Back issues