KaydedilenlerDerginizi ekleyin

Dergiler / Maltepe Journal of Mathematics / 2026 / Volume: 7 Issue: 1

Boundedness Of Involutions In Topological Algebras With Orthonormal Generalized Bases

Ramasamy Ct(Alagappa Government Arts College)0000-0002-2917-0092
Ganesa Moorthy C(Alagappa University)0000-0003-3119-7531
Ramkumar Solai(Alagappa Government Polytechnic College)0000-0001-5011-774X
Sayfa
—
Yayın Tarihi
2025-04-30
🏛️Bu makalenin bibliyografik verileri ve tam metin bağlantısı DergiPark üzerinden sağlanmıştır.
DergiPark Kaydı ↗
✨

Yapay Zeka Hızlı Bakış & Çıkarımlar

AI Insight
⚡ TL;DR(1 Cümlede Hızlı Çıkarım)

This result is obtained through a representation for involutions in these algebras.

📌 3 Maddede Bu Makale

🎯
Amaç & Hipotez:A main result of this article establishes that every involution in a sequentially complete locally convex topological algebra with an orthonormal generalized basis is bounded.
📊
Temel Bulgular & Veri:A main result of this article establishes that every involution in a sequentially complete locally convex topological algebra with an orthonormal generalized basis is bounded.
💡
Sonuç & Katkı:This result is obtained through a representation for involutions in these algebras.
🔬Tür:Research Article
📍Kapsam:Genişletilmiş Akademik Örneklem
⚙️Değişkenler:Net convergence · Automatic continuity · Schauder bases

Abstract

A main result of this article establishes that every involution in a sequentially complete locally convex topological algebra with an orthonormal generalized basis is bounded. This result is obtained through a representation for involutions in these algebras.

🔖

Bu Makaleye Atıf Yap

Ct, R., C, G. M., Solai, R. (2025). Boundedness Of Involutions In Topological Algebras With Orthonormal Generalized Bases. Maltepe Journal of Mathematics, Volume: 7 Issue: 1. https://doi.org/10.47087/mjm.1541646

📄 Tam Metin PDF Okuyucu

📄

PDF görüntüleyici hazırlanıyor...

Kaynakça (18)

  1. M. E. Azhari, Functional continuity of unital B0-algebras with orthogonal bases, Le matematiche, 72 (2017), 97-102
  2. V.K. Balachandran, Topological Algebras, North-Holland, Amsterdam, 2000.
  3. S. J. Bhatt and G. M. Deheri, Kothe spaces and topological algebra with bases, Proc. Indian Acad. Sci. (Math. Sci.), Vol. 100, No. 3, 1990, pp. 259-273
  4. S. J. Bhatt and G. M. Deheri, Orthogonal bases in a topological algebra are Schauder bases, Internat. J. Math. & Math. Sci. 15 (1992), 203-204
  5. P.G. Dixon and D.H. Fremlin, A remark concerning multiplicative functionals on LMC algebras, J. Lond. Math. Soc. 5 (1972) 231–232
  6. T. Husain, Positive functionals on topological algebras with bases, Math. Japonica, 28 (1983), 683-687.
  7. T. Husain, J. Liang, Multiplicative functionals on Frechet algebras with bases, Canad. J. Math. 29 (1977), 270-276
  8. T. Husain, J. Liang, Continuity of multiplicative linear functionals on Frechet algebras with bases, Bull. Soc. Roy. Sc Li´ege, 46 (1977), 8-11
  9. Husain T and Watson S, Topological algebras with orthogonal Schauder basis, Pacific J. Math. 91 (1980) 339-347
  10. Husain T and Watson S, Algebras with unconditional orthogonal basis, Proc. Am. Math. Soc. 79 (1980) 539-545
  11. S. Loganathan and C.G. Moorthy, A net convergence for Schauder double bases, Asian-Eur. J. Math. 9 (2016) 33 pp.
  12. E.A. Michael, Locally Multiplicatively Convex Topological Algebras, Mem. Amer. Math. Soc. 11, Amer. Math. Soc. Providence, RI, 1952.
  13. AR. Murugan, C. Ganesa Moorthy and CT. Ramasamy, Directed bases with net convergence, Surveys in Mathematics and its Applications, 19 (2024), 57 – 66.
  14. W. Rudin, Functional Analysis, Mc Graw Hill, New York, 1973.
  15. Z. Sawon and Z. Wronski, Fr´echet algebras with orthogonal bases, Colloq. Math. 48 (1984), 103-110
  16. I. Singer, Bases in Banach Spaces I, Springer, New York, 1970.
  17. G. Siva and C.G. Moorthy, Functional continuity of topological algebras with orthonormal bases, Asian-Eur. J. Math. 14 (2021) Article no. 2150059, 15 pp
  18. G. Siva, and C.G. Moorthy, Reviewed techniques in automatic continuity of linear functionals, Khayyam J. Math. 9 (2023), no. 1, 1-29