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Dergiler / Turkish Journal of Mathematics / 2005 / Cilt: 29 - Sayı: 2

2-quasi-$lambda$-nuclear maps

W SHATANAWI
Sayfa
157–167
Yayın Tarihi
2022-11-05
DOI
—
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⚡ TL;DR(1 Cümlede Hızlı Çıkarım)

For a nuclear $G_{infty}$ -space, we prove that a linear map T between normed spaces is 2-quasi-$lambda$ -nuclear if and only if it is quasi-$lambda$ -nuclear

📌 3 Maddede Bu Makale

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Amaç & Hipotez:In this paper we generalize the well-known result which says that the composition of quasi-nuclear maps is nuclear.
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Temel Bulgular & Veri:More precisely, we define what we call a 2-quasi-$lambda$ -nuclear map between normed spaces, and we prove that the composition of a 2-quasi-$lambda$ -nuclear map with a quasi- $lambda$ -nuclear map is a pseudo-$lambda$ -nuclear map.
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Sonuç & Katkı:For a nuclear $G_{infty}$ -space, we prove that a linear map T between normed spaces is 2-quasi-$lambda$ -nuclear if and only if it is quasi-$lambda$ -nuclear
🔬Tür:Araştırma Makalesi
📍Kapsam:Genişletilmiş Akademik Örneklem
⚙️Değişkenler:Alan Parametreleri

Abstract

In this paper we generalize the well-known result which says that the composition of quasi-nuclear maps is nuclear. More precisely, we define what we call a 2-quasi-$lambda$ -nuclear map between normed spaces, and we prove that the composition of a 2-quasi-$lambda$ -nuclear map with a quasi- $lambda$ -nuclear map is a pseudo-$lambda$ -nuclear map. Also, we prove that a quasi-$lambda$ -nuclear map is a 2-quasi-$lambda$ -nuclear map. For a nuclear $G_{infty}$ -space, we prove that a linear map T between normed spaces is 2-quasi-$lambda$ -nuclear if and only if it is quasi-$lambda$ -nuclear

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Bu Makaleye Atıf Yap

SHATANAWI, W. (2022). 2-quasi-$lambda$-nuclear maps. Turkish Journal of Mathematics, Cilt: 29 - Sayı: 2, 157–167. https://ajindex.com/articles/608744

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Kaynakça (8)

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  2. Kamthan, P.K.: Gupta, M.: Schauder Bases Behaviour and Stability, Indian Institute of Technology, Kanpur, 1988
  3. Köthe, G.: Topological Vector Spaces I and II, Springer-Verlag, Berlin-Heidelberg, New York (1969) and (1979)
  4. Pietsch, A.: Nuclear Locally Convex Spaces, Springer-Verlag, Berlin-Heidelberg, New York (1972)
  5. Pietsch, A.: Absolut p-summierende Abbildungenin normierten R ̈aumen, Studia Math., 28, 333-353 (1967)
  6. Ramanujan,M.S.: Power Series Spaces Ʌ(α) and Associated Ʌ(α)-Nuclearity, Math. Ann., 189, 161-168 (1970)
  7. Robinson, W.: Relationships Between λ-Nuclearity and Pseudo--Nuclearity, Trans. Amer.Math. Soc., 201, 291-303 (1975)
  8. Terzioglu, T.: Smooth Sequence Spaces and Associated Nuclearity, Proc. Amer. Math. Soc.,37, 497-504 (1973).