On formal power series over topological algebras
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Abstract
We present a general survey on formal power series over topological algebras, along with some perspectives which are not easily found in the literature.
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How to Cite
Weigt, M., & Zarakas, I. (2022). On formal power series over topological algebras. Extracta Mathematicae, 37(1), 57-74. https://doi.org/10.17398/2605-5686.37.1.57
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Section
Banach Spaces and Algebras
References
[1] G.R. Allan, A spectral theory for locally convex algebras, Proc. London Math. Soc. (3) 15 (1965), 399 – 421.
[2] G.R. Allan, On a class of locally convex algebras, Proc. London Math. Soc. (3) 17 (1967), 91 – 114.
[3] G.R. Allan, Embedding the algebra of formal power series in a Banach algebra, Proc. London Math. Soc. (3) 25 (1972), 329 – 340.
[4] G.R. Allan, Fréchet algebras and formal power series, Studia Math. 119 (1996), 271 – 288.
[5] R. Arens, The analytic functional calculus in commutative topological algebras, Pacific J. Math. 11 (1961), 405 – 429.
[6] F.F. Bonsall, J. Duncan, “ Complete Normed Algebras ”, Springer-Verlag, New York-Heidelberg, 1973.
[7] O. Bratteli, D.W. Robinson, Unbounded derivations of C∗ -algebras, Comm. Math. Phys. 42 (1975), 253 – 268.
[8] H.G. Dales, S.R. Patel, C.J. Read, Fréchet algebras of formal power series, in “ Banach Algebras 2009 ”, Banach Center Publications 91, Polish Academy of Sciences, Institute of Mathematics, Warsaw, 2010, 123 – 158.
[9] A.V. Ferreira, G. Tomassini, Finiteness properties of topological algebras, Ann. Scuola Norm. Sup. Pisa Cl. Sci. (4) 5 (1978), 471 – 488.
[10] M. Fragoulopoulou, “ Topological Algebras with Involution ”, North-Holland Mathematics Studies 200,Elsevier Science B.V., Amsterdam, 2005.
[11] L. Hörmander, “ An Introduction to Complex Analysis in Several Variables ”, D. Van Nostrand Co., Inc., Princeton, N.J.-Toronto, Ont.-London, 1966.
[12] T. Hungerford, “ Algebra ”, Graduate Texts in Mathematics 73, Springer-Verlag, New York-Berlin, 1980.
[13] B.E. Johnson, Continuity of derivations on commutative algebras, Amer. J. Math. 91 (1969), 1 – 10.
[14] H.H. Schaefer, “ Topological Vector Spaces ”, Springer Verlag, New York-Berlin, 1971.
[15] M.P. Thomas, The image of a derivation is contained in the radical, Ann. of Math. (2) 128 (1988), 435 – 460.
[16] M.P. Thomas, Local power series quotients of commutative Banach and Fréchet algebras, Trans. Amer. Math. Soc. 355 (2003), 2139 – 2160.
[17] M. Weigt, I. Zarakas, On domains of unbounded derivations of generalized B∗ -algebras, Banach J. Math. Anal. 12 (2018), 873 – 908.
[18] W. Zelazko, Metric generalizations of Banach algebras, Rozprawy Mat. 47 (1965), 70 pp.
[2] G.R. Allan, On a class of locally convex algebras, Proc. London Math. Soc. (3) 17 (1967), 91 – 114.
[3] G.R. Allan, Embedding the algebra of formal power series in a Banach algebra, Proc. London Math. Soc. (3) 25 (1972), 329 – 340.
[4] G.R. Allan, Fréchet algebras and formal power series, Studia Math. 119 (1996), 271 – 288.
[5] R. Arens, The analytic functional calculus in commutative topological algebras, Pacific J. Math. 11 (1961), 405 – 429.
[6] F.F. Bonsall, J. Duncan, “ Complete Normed Algebras ”, Springer-Verlag, New York-Heidelberg, 1973.
[7] O. Bratteli, D.W. Robinson, Unbounded derivations of C∗ -algebras, Comm. Math. Phys. 42 (1975), 253 – 268.
[8] H.G. Dales, S.R. Patel, C.J. Read, Fréchet algebras of formal power series, in “ Banach Algebras 2009 ”, Banach Center Publications 91, Polish Academy of Sciences, Institute of Mathematics, Warsaw, 2010, 123 – 158.
[9] A.V. Ferreira, G. Tomassini, Finiteness properties of topological algebras, Ann. Scuola Norm. Sup. Pisa Cl. Sci. (4) 5 (1978), 471 – 488.
[10] M. Fragoulopoulou, “ Topological Algebras with Involution ”, North-Holland Mathematics Studies 200,Elsevier Science B.V., Amsterdam, 2005.
[11] L. Hörmander, “ An Introduction to Complex Analysis in Several Variables ”, D. Van Nostrand Co., Inc., Princeton, N.J.-Toronto, Ont.-London, 1966.
[12] T. Hungerford, “ Algebra ”, Graduate Texts in Mathematics 73, Springer-Verlag, New York-Berlin, 1980.
[13] B.E. Johnson, Continuity of derivations on commutative algebras, Amer. J. Math. 91 (1969), 1 – 10.
[14] H.H. Schaefer, “ Topological Vector Spaces ”, Springer Verlag, New York-Berlin, 1971.
[15] M.P. Thomas, The image of a derivation is contained in the radical, Ann. of Math. (2) 128 (1988), 435 – 460.
[16] M.P. Thomas, Local power series quotients of commutative Banach and Fréchet algebras, Trans. Amer. Math. Soc. 355 (2003), 2139 – 2160.
[17] M. Weigt, I. Zarakas, On domains of unbounded derivations of generalized B∗ -algebras, Banach J. Math. Anal. 12 (2018), 873 – 908.
[18] W. Zelazko, Metric generalizations of Banach algebras, Rozprawy Mat. 47 (1965), 70 pp.