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New Condition of Automatic Continuity of Dense Range Homomorphisms on Jordan – Banach Algebras | ||
| Journal of Education and Science | ||
| Article 9, Volume 27, Issue 4, 2018, Pages 146-150 PDF (0 K) | ||
| DOI: 10.33899/edusj.2018.159292 | ||
| Authors | ||
| RUQAYAH N. BALO; NADIA A. ABDULRAZAQ; DUAA F. ABDULLAH | ||
| Abstract | ||
| The following open problem stated that, if T: A⟶B is a dense range homomorphism between Banach algebras A and B such that B is semi-simple. Is T automatically continuous? (see [1]). In [3] given a partial solution of the above problem as follows: Let A and B be Fréchet algebras such that B is semi simple, the spectral radius rB is continuous on B and the spectral radius rA is continuous at zero. If T : A ⟶ B is a dense range homomorphism, then T is automatically continuous. In this paper, we prove the following result : If T : A+ ⟶ B+ is a dense range homomorphism between Jordan – Banach algebras A+ and B+ such that B+ is semi simple, the spectral radius rB+ is continuous on B+ and the spectral rA+ is continuous at zero, then T is automatically continuous. | ||
| Keywords | ||
| automatic continuity; Dense Range Homomorphisms; Banach Algebras | ||
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