# Shital Patel

# India

C. U. Shah University

Link for [DPR]: https://www.impan.pl/en/publishing-house/banach-center-publications/all/91/0/86359/frechet-algebras-of-power-series

Link for [P]: https://arxiv.org/abs/2006.11134v3

List of References used in SCS 2022 Slide set

[Ar] Arens, R., Dense inverse limit rings, Michigan Math. J. 5 (1958), 169-182.

[C1] Carpenter, R.L., Uniqueness of topology for commutative semisimple F-algebras, Proc. Amer. Math. Soc. 29 (1971), 113-117.

[C2] Carpenter, R.L., Continuity of derivations on F-algebras, Amer. J. Math. 93 (1971), 500-502.

[Cl] Clayton, D., A reduction of the continous homomorphism problem for F-algebras, Rocky Mountain J. Math. 5 (1975), 337-344.

[D] Dales, H.G., Automatic continuity: a survey, Bull. London Math. Soc. 10 (1978), 129-183.

[DE] Dixon, P.G. and Esterle, J., Michael’s problem and the Poincaré-Fatou-Bieberbach phenomenon, Bull. Amer. Math. Soc. 15 (1986), 127-187.

[DF] Dixon, P.G. and Fremlin, D.H., A remark concerning multiplicative functionals on LMC algebras, J. London Math. Soc. 5 (1972), 231- 232.

[E] Esterle, J., Picard’s theorem, Mittag-Leffler methods, and continuity of characters on Fréchet algebras, Ann. Sci. Ecole. Norm. Sup. 29 (1996), 539-582.

[L] Loy, R.J., Commutative Banach algebras with non-unique complete norm topology, Bull. Austral. Math. Soc. 10 (1974), 409-420.

[P1] Patel, S.R., Fréchet algebras, formal power series, and automatic continuity, Studia Math. 187 (2008), 125-136.

[P2] Patel, S.R., Uniqueness of the Fréchet algebra topology on certain Fréchet algebras, Studia Math. 234 (2016), 31-47.

[P3] Patel, S.R., On discontinuity of derivations, inducing non-unique complete metric topologies, Refereed preprint. arXiv: 2002-06365.

[P4] Patel, S.R., On avatars of the Singer-Wermer conjectures in Fréchet algebras, In: Proceedings of the ICTAA 2021, 121-137, Mathematics Studies 8, Tartu (Estonia), 2021.

[R] Read, C.J., Derivations with large separating subspace, Proc. Amer. Math. Soc. 130 (2002), 3671-3677.

[T] Thomas, M.P., The image of a derivation is contained in the radical, Ann. of Math. 128 (1988), 435-460.