Almost isometric ideals and non-separable Gurariy spaces

Authors

Pradipta Bandyopadhyay, Indian Statistical Institute, Kolkata
S. Dutta, Indian Institute of Technology Kanpur
A. Sensarma, Indian Institute of Technology Kanpur

Article Type

Research Article

Publication Title

Journal of Mathematical Analysis and Applications

Abstract

The main result of this short note is that a (non-separable) Banach space is a Gurariy space if and only if every separable almost isometric ideal in X is isometric to the separable Gurariy space G. We also obtain a similar characterization of L1-predual spaces in terms of ideals. Along the way, we show that the family of ideals/almost isometric ideals in a Banach space is closed under increasing limits. And hence, the family of all separable ideals/almost isometric ideals in a Banach space is a skeleton.

First Page

279

Last Page

284

DOI

10.1016/j.jmaa.2018.02.013

Publication Date

6-1-2018

Comments

All Open Access, Bronze

Recommended Citation

Bandyopadhyay, Pradipta; Dutta, S.; and Sensarma, A., "Almost isometric ideals and non-separable Gurariy spaces" (2018). Journal Articles. 1369.
https://digitalcommons.isical.ac.in/journal-articles/1369