AUTOMATIC CONTINUITY OF HOMOMORPHISMS BETWEEN BANACH ALGEBRAS AND FR´ECHET ALGEBRAS

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GHASEMI HONARY T.

مرکز اطلاعات علمی Scientific Information Database (SID) - Trusted Source for Research and Academic Resources

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Journal: Bulletin of the Iranian Mathematical Society Year:2006 | Volume:32 | Issue:2 Page(s): 1-11

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Title

AUTOMATIC CONTINUITY OF HOMOMORPHISMS BETWEEN BANACH ALGEBRAS AND FR´ECHET ALGEBRAS

Author(s)

GHASEMI HONARY T. | Issue Writer Certificate

Keywords

SEMISIMPLE ALGEBRAS

BANACH AND FRÉCHET ALGEBRAS

AUTOMATIC CONTINUITY

UNIQUENESS OF NORM AND TOPOLOGY

DENSE RANGE HOMOMORPHISM

SPECTRAL RADIUS

Abstract

In 1989, T. J. Ransford presented a short proof of Johnson's uniqueness of norm theorem. We follow the same method to show that if A and B are Fréchet algebras, B is semisimple and T: A → B is a surjective homomorphism with a certain condition, then T is continuous. In particular, when A is a Banach algebra we conclude that every epimorphism T: A → B is automatically continuous and hence every semisimple Banach algebra has a unique topology as a Fréchet algebra, which is an extension of Johnson's uniqueness of norm theorem.If A and B are Banach algebras, B is semisimple and T: A → B is a DENSE RANGE HOMOMORPHISM, then the continuity of T is a long-standing open question. In this work we give a positive answer to this open question with an extra condition on B and then present a partial answer to the well-known Michael's problem. We also obtain similar results for DENSE RANGE HOMOMORPHISMs of Fréchet algebras. Finally, we show that if the above question on the continuity of DENSE RANGE HOMOMORPHISMs of Banach algebras has a positive answer then the same question has a positive answer for Fréchet algebras.

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APA: Copy

GHASEMI HONARY, T.. (2006). AUTOMATIC CONTINUITY OF HOMOMORPHISMS BETWEEN BANACH ALGEBRAS AND FR´ECHET ALGEBRAS. BULLETIN OF THE IRANIAN MATHEMATICAL SOCIETY, 32(2), 1-11. SID. https://sid.ir/paper/529707/en

Vancouver: Copy

GHASEMI HONARY T.. AUTOMATIC CONTINUITY OF HOMOMORPHISMS BETWEEN BANACH ALGEBRAS AND FR´ECHET ALGEBRAS. BULLETIN OF THE IRANIAN MATHEMATICAL SOCIETY[Internet]. 2006;32(2):1-11. Available from: https://sid.ir/paper/529707/en

IEEE: Copy

T. GHASEMI HONARY, “AUTOMATIC CONTINUITY OF HOMOMORPHISMS BETWEEN BANACH ALGEBRAS AND FR´ECHET ALGEBRAS,” BULLETIN OF THE IRANIAN MATHEMATICAL SOCIETY, vol. 32, no. 2, pp. 1–11, 2006, [Online]. Available: https://sid.ir/paper/529707/en

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