Analyse fonctionnelle
Norm-Controlled Inversion of Banach algebras of infinite matrices
Comptes Rendus. Mathématique, Tome 358 (2020) no. 4, pp. 407-414.

In this paper we provide a polynomial norm-controlled inversion of Baskakov–Gohberg–Sjöstrand Banach algebra in a Banach algebra ( q ), 1q, which is not a symmetric *- Banach algebra.

Reçu le :
Révisé le :
Accepté le :
Publié le :
DOI : 10.5802/crmath.54
Classification : 47G10, 45P05, 47B38, 31B10, 46E30
Fang, Qiquan 1 ; Shin, Chang Eon 2

1 Department of Mathematics, Zhejiang University of Science and Technology, Hangzhou, Zhejiang, 310023, China
2 Chang Eon Shin: Department of Mathematics, Sogang University, Seoul, 04107, Korea. Email: shinc@sogang.ac.kr
@article{CRMATH_2020__358_4_407_0,
     author = {Fang, Qiquan and Shin, Chang Eon},
     title = {Norm-Controlled {Inversion} of {Banach} algebras of infinite matrices},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {407--414},
     publisher = {Acad\'emie des sciences, Paris},
     volume = {358},
     number = {4},
     year = {2020},
     doi = {10.5802/crmath.54},
     language = {en},
     url = {http://archive.numdam.org/articles/10.5802/crmath.54/}
}
TY  - JOUR
AU  - Fang, Qiquan
AU  - Shin, Chang Eon
TI  - Norm-Controlled Inversion of Banach algebras of infinite matrices
JO  - Comptes Rendus. Mathématique
PY  - 2020
SP  - 407
EP  - 414
VL  - 358
IS  - 4
PB  - Académie des sciences, Paris
UR  - http://archive.numdam.org/articles/10.5802/crmath.54/
DO  - 10.5802/crmath.54
LA  - en
ID  - CRMATH_2020__358_4_407_0
ER  - 
%0 Journal Article
%A Fang, Qiquan
%A Shin, Chang Eon
%T Norm-Controlled Inversion of Banach algebras of infinite matrices
%J Comptes Rendus. Mathématique
%D 2020
%P 407-414
%V 358
%N 4
%I Académie des sciences, Paris
%U http://archive.numdam.org/articles/10.5802/crmath.54/
%R 10.5802/crmath.54
%G en
%F CRMATH_2020__358_4_407_0
Fang, Qiquan; Shin, Chang Eon. Norm-Controlled Inversion of Banach algebras of infinite matrices. Comptes Rendus. Mathématique, Tome 358 (2020) no. 4, pp. 407-414. doi : 10.5802/crmath.54. http://archive.numdam.org/articles/10.5802/crmath.54/

[1] Baskakov, Anatoly G. Wiener’s theorem and asymptotic estimates for elements of inverse matrices, Funkts. Anal. Prilozh., Volume 24 (1990) no. 3, pp. 64-65 translation in Funct. Anal. Appl. 24 (1990), no. 3, p. 222-224 | MR | Zbl

[2] Baskakov, Anatoly G. Asymptotic estimates for elements of matrices of inverse operators, and harmonic analysis, Sib. Mat. Zh., Volume 38 (1997) no. 1, pp. 14-28 translation in Sib. Math. J. 38 (1997), no. 1, p. 10-22 | MR | Zbl

[3] Brandenburg, L. H. On identifying the maximal ideals in Banach Algebras, J. Math. Anal. Appl., Volume 50 (1975), pp. 489-510 | DOI | MR | Zbl

[4] Gröchenig, Karlheinz Wiener’s lemma: theme and variations, an introduction to spectral invariance and its applications, Four Short Courses on Harmonic Analysis: Wavelets, Frames, Time-Frequency Methods, and Applications to Signal and Image Analysis (Applied and Numerical Harmonic Analysis), Birkhäuser, 2010 | DOI | Zbl

[5] Gröchenig, Karlheinz; Klotz, Andreas Noncommutative approximation: inverse-closed subalgebras and off-diagonal decay of matrices, Constr. Approx., Volume 32 (2010) no. 3, pp. 429-466 | DOI | MR | Zbl

[6] Gröchenig, Karlheinz; Klotz, Andreas Norm-controlled inversion in smooth Banach algebras. I, J. Lond. Math. Soc., Volume 88 (2013) no. 1, pp. 49-64 | DOI | MR | Zbl

[7] Gröchenig, Karlheinz; Klotz, Andreas Norm-controlled inversion in smooth Banach algebras. II, Math. Nachr., Volume 287 (2014) no. 8-9, pp. 917-937 | DOI | MR | Zbl

[8] Jaffard, Stéphane Propriétés des matrices “bien localisées” près de leur diagonale et quelques applications, Ann. Inst. Henri Poincaré, Anal. Non Linéaire, Volume 7 (1990) no. 5, pp. 461-476 | DOI | Numdam | Zbl

[9] Nikolski, Nikolai In search of the invisible spectrum, Ann. Inst. Fourier, Volume 49 (1999) no. 6, pp. 1925-1966 | DOI | Numdam | MR | Zbl

[10] Rim, Kyung Soo; Shin, Chang Eon; Sun, Qiyu Stability of localized integral operators on weighted L p spaces, Numer. Funct. Anal. Optim., Volume 33 (2012) no. 7-9, pp. 1166-1193 | MR | Zbl

[11] Samei, Ebrahim; Shepelska, Varvara Norm-controlled inversion in weighted convolution algebras, J. Fourier Anal. Appl., Volume 25 (2019) no. 6, pp. 3018-3044 | DOI | MR | Zbl

[12] Shin, Chang Eon; Sun, Qiyu Differential subalgebras and norm-controlled inversion (2019) (submitted, https://arxiv.org/abs/1911.08679)

[13] Shin, Chang Eon; Sun, Qiyu Polynomial control on stability, J. Funct. Anal., Volume 276 (2019) no. 1, pp. 148-182 | DOI | Zbl

[14] Sjöstrand, Johannes Wiener type algebra of pseudodifferential operators, Sémin. Équ. Dériv. Partielles, Volume 1994-1995 (1995), 4, 19 pages | Zbl

[15] Sun, Qiyu Wiener’s lemma for infinite matrices with polynomial off-diagonal decay, C. R. Math. Acad. Sci. Paris, Volume 340 (2005), pp. 567-570 | MR | Zbl

[16] Sun, Qiyu Wiener’s lemma for infinite matrices, Trans. Am. Math. Soc., Volume 359 (2007) no. 7, pp. 3099-3123 | MR | Zbl

[17] Sun, Qiyu Wiener’s lemma for localized integral operators, Appl. Comput. Harmon. Anal., Volume 25 (2008) no. 2, pp. 148-167 | MR | Zbl

[18] Sun, Qiyu Wiener’s lemma for infinite matrices. II., Constr. Approx., Volume 34 (2011) no. 2, pp. 209-235 | MR | Zbl

[19] Wiener, Norbert Tauberian theorem, Ann. Math., Volume 33 (1932), pp. 1-100 | DOI | MR | Zbl

Cité par Sources :