Invertible extensions and growth conditions

Catalin Badea; Vladimir Müller

doi:10.1016/j.crma.2004.04.011

Mathematical Analysis

Invertible extensions and growth conditions

Presented by: Jean-Pierre Kahane

Catalin Badea ¹; Vladimir Müller ²

¹ Département de mathématiques, UMR CNRS no. 8524, université Lille I, 59655 Villeneuve d'Ascq, France
² Institute of Mathematics AV CR, Zitna 25, 115 67 Prague 1, Czech Republic

Comptes Rendus. Mathématique, Volume 339 (2004) no. 1, pp. 21-26.

Abstract
Résumé

We study invertible extensions of Banach and Hilbert space bounded linear operators with prescribed growth conditions for the norm of inverses. In particular, the solutions of some open problems are obtained.

Nous étudions les extensions inversibles des opérateurs linéaires et bornés sur un espace de Banach ou de Hilbert avec des conditions de croissance données pour les normes des inverses. Nous obtenons en particulier la réponse à plusieurs problèmes ouverts formulés dans la literature.

Received: 2004-03-02
Accepted: 2004-04-06
Published online: 2004-05-20

DOI: 10.1016/j.crma.2004.04.011

Author's affiliations:

Catalin Badea ¹; Vladimir Müller ²

¹ Département de mathématiques, UMR CNRS no. 8524, université Lille I, 59655 Villeneuve d'Ascq, France
² Institute of Mathematics AV CR, Zitna 25, 115 67 Prague 1, Czech Republic

@article{CRMATH_2004__339_1_21_0,
     author = {Catalin Badea and Vladimir M\"uller},
     title = {Invertible extensions and growth conditions},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {21--26},
     publisher = {Elsevier},
     volume = {339},
     number = {1},
     year = {2004},
     doi = {10.1016/j.crma.2004.04.011},
     language = {en},
}

TY  - JOUR
AU  - Catalin Badea
AU  - Vladimir Müller
TI  - Invertible extensions and growth conditions
JO  - Comptes Rendus. Mathématique
PY  - 2004
SP  - 21
EP  - 26
VL  - 339
IS  - 1
PB  - Elsevier
DO  - 10.1016/j.crma.2004.04.011
LA  - en
ID  - CRMATH_2004__339_1_21_0
ER  -

%0 Journal Article
%A Catalin Badea
%A Vladimir Müller
%T Invertible extensions and growth conditions
%J Comptes Rendus. Mathématique
%D 2004
%P 21-26
%V 339
%N 1
%I Elsevier
%R 10.1016/j.crma.2004.04.011
%G en
%F CRMATH_2004__339_1_21_0

Catalin Badea; Vladimir Müller. Invertible extensions and growth conditions. Comptes Rendus. Mathématique, Volume 339 (2004) no. 1, pp. 21-26. doi : 10.1016/j.crma.2004.04.011. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2004.04.011/

References
Cited by

[1] R. Arens Inverse-producing extensions of normed algebras, Trans. Amer. Math. Soc., Volume 88 (1958), pp. 536-548

[2] C. Badea Perturbations of operators similar to contractions and the commutator equation, Studia Math., Volume 150 (2002), pp. 273-293

[3] C. Badea, V. Müller, Growth conditions and inverse producing extensions, Preprint

[4] I. Colojoară; C. Foiaş Theory of Generalized Spectral Operators, Math. Appl., vol. 9, Gordon and Breach, New York, 1968

[5] M. Didas $ℰ (𝕋^{n})$ -subscalar n-tuples and the Cesaro operator on H^p, Ann. Univ. Sarav. Ser. Math., Volume 10 (2000) no. 2, p. i-iii (and 284–335)

[6] R.G. Douglas On extending commutative semigroups of isometries, Bull. London Math. Soc., Volume 1 (1969), pp. 157-159

[7] J. Eschmeier; M. Putinar Spectral Decompositions and Analytic Sheaves, London Math. Soc. Monographs (N.S.), vol. 10, The Clarendon Press, Oxford University Press, New York, 1996

[8] J. Esterle Uniqueness, strong forms of uniqueness and negative powers of contractions, (Warsaw, 1992) (Banach Center Publ.), Volume vol. 30, Polish Acad. Science, Warsaw (1994), pp. 127-145

[9] H.A. Gindler; A.E. Taylor The minimum modulus of a linear operator and its use in spectral theory, Studia Math., Volume 22 (1962/1963), pp. 15-41

[10] C. Herz The theory of p-spaces with an application to convolution operators, Trans. Amer. Math. Soc., Volume 154 (1971), pp. 69-82

[11] K. Kellay Contractions et hyperdistributions à spectre de Carleson, J. London Math. Soc. (2), Volume 58 (1998), pp. 185-196

[12] S. Kwapień On operators factorizable through L_p space, (Univ. de Bordeaux, 1971) (Mém. Soc. Math. France), Volume vol. 31–32, Soc. Math. France, Paris (1972), pp. 215-225

[13] K.B. Laursen; M.M. Neumann An Introduction to Local Spectral Theory, London Math. Soc. Monographs (N.S.), vol. 20, The Clarendon Press, Oxford University Press, New York, 2000

[14] T.L. Miller; V.G. Miller; M.M. Neumann Growth conditions and decomposable extensions, (Memphis, TN, 2001) (Contemp. Math.), Volume vol. 321, American Mathematical Society, Providence, RI (2003), pp. 197-205

[15] T.L. Miller; V. Miller; M.M. Neumann Spectral subspaces of subscalar and related operators, Proc. Amer. Math. Soc., Volume 132 (2004), pp. 1483-1493

[16] T.L. Miller, V. Miller, M.M. Neumann, Local spectral properties of weighted shifts, J. Operator Theory, in press

[17] T.L. Miller; V.G. Miller; M.M. Neumann Localization in the spectral theory of operators on Banach spaces, (Edwardsville, IL, 2002) (Contemp. Math.), Volume vol. 328, American Mathematical Society, Providence, RI (2003), pp. 247-262

[18] V. Müller Adjoining inverses to noncommutative Banach algebras and extensions of operators, Studia Math., Volume 91 (1988), pp. 73-77

[19] C.J. Read Spectrum reducing extension for one operator on a Banach space, Trans. Amer. Math. Soc., Volume 308 (1988), pp. 413-429

[20] C.J. Read Extending an operator from a Hilbert space to a larger Hilbert space, so as to reduce its spectrum, Israel J. Math., Volume 57 (1987), pp. 375-380

[21] B. Sz.-Nagy; C. Foiaş Harmonic Analysis of Operators on Hilbert Space, North-Holland, Amsterdam, 1970 (Translated from the French and revised)

[22] M. Zarrabi Contractions à spectre dénombrable et propriétés d'unicité des fermés dénombrables du cercle, Ann. Inst. Fourier (Grenoble), Volume 43 (1993), pp. 251-263

Cited by Sources:

Comments - Politique