[KSCI] Korea Science Citation Index Service

http://dx.doi.org/10.4134/JKMS.j180151

THE IDEAL OF WEAKLY p-NUCLEAR OPERATORS AND ITS INJECTIVE AND SURJECTIVE HULLS

Kim, Ju Myung (Department of Mathematics Sejong University)

Publication Information

Journal of the Korean Mathematical Society / v.56, no.1, 2019 , pp. 225-237 More about this Journal

Abstract

We introduce a larger ideal ${\mathcal{N}}_{wp}$ of the ideal of p-nuclear operators. We obtain isometric representations of the injective and surjective hulls of ${\mathcal{N}}_{wp}$ and study them.

Keywords

Banach operator ideal; tensor norm; nuclear operator;

Citations & Related Records

Reference

1	A. Defant and K. Floret, Tensor Norms and Operator Ideals, North-Holland Mathematics Studies, 176, North-Holland Publishing Co., Amsterdam, 1993.
2	J. M. Delgado, C. Pineiro, and E. Serrano, Density of finite rank operators in the Banach space of p-compact operators, J. Math. Anal. Appl. 370 (2010), no. 2, 498-505. DOI
3	J. M. Delgado, C. Pineiro, and E. Serrano, Operators whose adjoints are quasi p-nuclear, Studia Math. 197 (2010), no. 3, 291-304. DOI
4	J. Diestel, H. Jarchow, and A. Tonge, Absolutely Summing Operators, Cambridge Studies in Advanced Mathematics, 43, Cambridge University Press, Cambridge, 1995.
5	J. H. Fourie, Injective and surjective hulls of classical p-compact operators with application to unconditionally p-compact operators, Studia Math. 240 (2018), no. 2, 147-159. DOI
6	J. M. Kim, Unconditionally p-null sequences and unconditionally p-compact operators, Studia Math. 224 (2014), no. 2, 133-142. DOI
7	J. Fourie and J. Swart, Banach ideals of p-compact operators, Manuscripta Math. 26 (1978/79), no. 4, 349-362. DOI
8	J. Fourie and J. Swart, Tensor products and Banach ideals of p-compact operators, Manuscripta Math. 35 (1981), no. 3, 343-351. DOI
9	D. Galicer, S. Lassalle, and P. Turco, The ideal of p-compact operators: a tensor product approach, Studia Math. 211 (2012), no. 3, 269-286. DOI
10	J. M. Kim, The ideal of unconditionally p-compact operators, Rocky Mountain J. Math. 47 (2017), no. 7, 2277-2293. DOI
11	A. Persson and A. Pietsch, p-nukleare une p-integrale Abbildungen in Banachraumen, Studia Math. 33 (1969), 19-62. DOI
12	A. Pietsch, Operator Ideals, translated from German by the author, North-Holland Mathematical Library, 20, North-Holland Publishing Co., Amsterdam, 1980.
13	N. Tomczak-Jaegermann, Banach-Mazur Distances and Finite-Dimensional Operator Ideals, Pitman Monographs and Surveys in Pure and Applied Mathematics, 38, Longman Scientific & Technical, Harlow, 1989.
14	D. P. Sinha and A. K. Karn, Compact operators whose adjoints factor through subspaces of $l_p$ , Studia Math. 150 (2002), no. 1, 17-33. DOI