Conditions are given for Banach algebras A and Banach algebras B which insure that every homomorphism T from A into B is automatic continuous. Similar results are obtained for derivations which either map the algebra A into itself.
| Published in | Pure and Applied Mathematics Journal (Volume 4, Issue 2) |
| DOI | 10.11648/j.pamj.20150402.12 |
| Page(s) | 43-46 |
| Creative Commons |
This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited. |
| Copyright |
Copyright © The Author(s), 2024. Published by Science Publishing Group |
*-Algebra, *Prime Algebra, *-Simple Algebra, Automatic Continuity, Separting Space
| [1] | F.F. Bonsall and J. Duncan, Complete normed algebras, Spring6 Verlag. Berlin (1973). |
| [2] | J. Cusack, Automatic Continuity and topologically simple Banach algebras, J. London. Math. Soc (2), 16 (1977), 439-500. |
| [3] | R. V. Garimella, Continuity of derivation on some semi-prime Banach algebra, Proc. Amer. Math. Soc., 99 (1987), 289 [12]-292. |
| [4] | R.V. Garimella, Prime ideals and the continuity of derivation on integral domins, Indian. J. Pure app. Math, 22 (12) (1991), 1013-1018. |
| [5] | R.V. Garimella, On nilpotenty of the separting ideal of a derivation. Proc. Amer. Math. Soc., 117, (1993), 167-174. |
| [6] | N. Jacobson, Basic Algebra II, W. H. Ferman and Compagny (1980). |
| [7] | B.E Johnson, The uniqueness of the (complete) norm topology, Bull. Amer. Math. Soc. 73, (1967) 537-539 |
| [8] | B.E Johnson, and A. M. Sinclair, Continuity of derivation and a problem of Kaplansky, Amer. J. Math. Math. 90 (1968), 1067-1073. |
| [9] | M. Mathieu et V. Runde, Derivations mapping into the radical II, Bull. London Math. Soc., 24(1992), 485-487. |
| [10] | V. Runde, Continuity of derivations and epimorphisms, Pacific J. of Math., Vol. 147, Nr. 2 (1991), 365-374. |
| [11] | A. M. Sinclair, Automatic Continuity of linear operators, London. Math. Soc. Lecture Note Series 21 (C.U.P., Combridge 1976). |
| [12] | Y. TIDLI, L. OUKHTITE, A. TAJMOUATI, On the Automatic continuity of the epimorphisms in *algebras of Banach. IJMMS 2004: 22 1183-1187 (2002). |
APA Style
Youssef Tidli. (2015). The Automatic Continuity of Linear Operators on Some Semi-Prime Banach Algebra. Pure and Applied Mathematics Journal, 4(2), 43-46. https://doi.org/10.11648/j.pamj.20150402.12
ACS Style
Youssef Tidli. The Automatic Continuity of Linear Operators on Some Semi-Prime Banach Algebra. Pure Appl. Math. J. 2015, 4(2), 43-46. doi: 10.11648/j.pamj.20150402.12
AMA Style
Youssef Tidli. The Automatic Continuity of Linear Operators on Some Semi-Prime Banach Algebra. Pure Appl Math J. 2015;4(2):43-46. doi: 10.11648/j.pamj.20150402.12
Share This Article
Twitter
Linked In
Facebook
Copy
Download@article{10.11648/j.pamj.20150402.12,
author = {Youssef Tidli},
title = {The Automatic Continuity of Linear Operators on Some Semi-Prime Banach Algebra},
journal = {Pure and Applied Mathematics Journal},
volume = {4},
number = {2},
pages = {43-46},
doi = {10.11648/j.pamj.20150402.12},
url = {https://doi.org/10.11648/j.pamj.20150402.12},
eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.pamj.20150402.12},
abstract = {Conditions are given for Banach algebras A and Banach algebras B which insure that every homomorphism T from A into B is automatic continuous. Similar results are obtained for derivations which either map the algebra A into itself.},
year = {2015}
}
TY - JOUR T1 - The Automatic Continuity of Linear Operators on Some Semi-Prime Banach Algebra AU - Youssef Tidli Y1 - 2015/02/11 PY - 2015 N1 - https://doi.org/10.11648/j.pamj.20150402.12 DO - 10.11648/j.pamj.20150402.12 T2 - Pure and Applied Mathematics Journal JF - Pure and Applied Mathematics Journal JO - Pure and Applied Mathematics Journal SP - 43 EP - 46 PB - Science Publishing Group SN - 2326-9812 UR - https://doi.org/10.11648/j.pamj.20150402.12 AB - Conditions are given for Banach algebras A and Banach algebras B which insure that every homomorphism T from A into B is automatic continuous. Similar results are obtained for derivations which either map the algebra A into itself. VL - 4 IS - 2 ER -
Information
Email: