# Interpolation of the measure of non-compactness by the real method

Fernando Cobos; Pedro Fernández-Martínez; Antón Martínez

Studia Mathematica (1999)

- Volume: 135, Issue: 1, page 25-38
- ISSN: 0039-3223

## Access Full Article

top## Abstract

top## How to cite

topCobos, Fernando, Fernández-Martínez, Pedro, and Martínez, Antón. "Interpolation of the measure of non-compactness by the real method." Studia Mathematica 135.1 (1999): 25-38. <http://eudml.org/doc/216641>.

@article{Cobos1999,

abstract = {We investigate the behaviour of the measure of non-compactness of an operator under real interpolation. Our results refer to general Banach couples. An application to the essential spectral radius of interpolated operators is also given.},

author = {Cobos, Fernando, Fernández-Martínez, Pedro, Martínez, Antón},

journal = {Studia Mathematica},

keywords = {measure of non-compactness; real interpolation},

language = {eng},

number = {1},

pages = {25-38},

title = {Interpolation of the measure of non-compactness by the real method},

url = {http://eudml.org/doc/216641},

volume = {135},

year = {1999},

}

TY - JOUR

AU - Cobos, Fernando

AU - Fernández-Martínez, Pedro

AU - Martínez, Antón

TI - Interpolation of the measure of non-compactness by the real method

JO - Studia Mathematica

PY - 1999

VL - 135

IS - 1

SP - 25

EP - 38

AB - We investigate the behaviour of the measure of non-compactness of an operator under real interpolation. Our results refer to general Banach couples. An application to the essential spectral radius of interpolated operators is also given.

LA - eng

KW - measure of non-compactness; real interpolation

UR - http://eudml.org/doc/216641

ER -

## References

top- [1] E. Albrecht, Spectral interpolation, in: Oper. Theory Adv. Appl. 14, Birkhäuser, Basel, 1984.
- [2] J. Bergh and J. Löfström, Interpolation Spaces. An Introduction, Springer, Berlin, 1976. Zbl0344.46071
- [3] B. Carl and I. Stephani, Entropy, Compactness and the Approximation of Operators, Cambridge Univ. Press, Cambridge, 1990.
- [4] F. Cobos, D. E. Edmunds and A. J. B. Potter, Real interpolation and compact linear operators, J. Funct. Anal. 88 (1990), 351-365. Zbl0704.46049
- [5] F. Cobos, T. Kühn and T. Schonbek, One-sided compactness results for Aronszajn-Gagliardo functors, ibid. 106 (1992), 274-313. Zbl0787.46061
- [6] F. Cobos and J. Peetre, Interpolation of compactness using Aronszajn-Gagliardo functors, Israel J. Math. 68 (1989), 220-240. Zbl0716.46054
- [7] F. Cobos and J. Peetre, Interpolation of compact operators: The multidimensional case, Proc. London Math. Soc. 63 (1991), 371-400. Zbl0702.46047
- [8] F. Cobos and L. E. Persson, Real interpolation of compact operators between quasi-Banach spaces, Math. Scand. 82 (1998), 138-160. Zbl0921.46084
- [9] M. Cwikel, Real and complex interpolation and extrapolation of compact operators, Duke Math. J. 65 (1992), 333-343. Zbl0787.46062
- [10] D. E. Edmunds and W. D. Evans, Spectral Theory and Differential Operators, Clarendon Press, Oxford, 1987. Zbl0628.47017
- [11] M. A. Krasnosel'skiĭ, On a theorem of M. Riesz, Soviet Math. Dokl. 1 (1960), 229-231.
- [12] M. A. Krasnosel'skiĭ, P. P. Zabreĭko, E. I. Pustyl'nik and P. E. Sobolevskiĭ, Integral Operators in Spaces of Summable Functions, Noordhoff, Leiden, 1976.
- [13] R. D. Nussbaum, The radius of the essential spectrum, Duke Math. J. 37 (1970), 473-479. Zbl0216.41602
- [14] A. Pietsch, Operator Ideals, North-Holland, Amsterdam, 1980.
- [15] M. F. Teixeira and D. E. Edmunds, Interpolation theory and measures of non-compactness, Math. Nachr. 104 (1981), 129-135. Zbl0492.46062
- [16] H. Triebel, Interpolation Theory, Function Spaces, Differential Operators, North-Holland, Amsterdam, 1978. Zbl0387.46033

## NotesEmbed ?

topTo embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.