Annales Academiæ Scientiarum Fennicæ
Mathematica
Volumen 45, 2020, 863–876

THE IDEAL OF WEAKLY p-COMPACT OPERATORS AND ITS APPROXIMATION PROPERTY FOR BANACH SPACES

Ju Myung Kim

Sejong University, Department of Mathematics
Seoul 05006, Korea; kjm21 'at' sejong.ac.kr

Abstract. We investigate the ideal W_p of weakly p-compact operators and its approximation property (W_p-AP). We prove that

W_p = W_p o W_p and V_p = K_up o W_p^-1 and that for 1 < p ≤ ∞, a Banach space X has the W_p-AP if and only if the identity map on X is approximated by finite rank operators on X in the topology of uniform convergence on weakly p-compact sets. Also, we study the W_p-AP for classical sequence spaces and dual spaces.

2010 Mathematics Subject Classification: Primary 46B28, 46B45, 47L20.

Key words: Weakly p-compact set, the ideal of weakly p-compact operators, the W_p-approximation property.

Reference to this article: J. M. Kim: The ideal of weakly p-compact operators and its approximation property for Banach spaces. Ann. Acad. Sci. Fenn. Math. 45 (2020), 863–876.

Full document as PDF file

https://doi.org/10.5186/aasfm.2020.4547