Skip to main content Accessibility help
×
Home

THE POSITION OF $\mathcal{K}(X,Y)$ IN $\mathcal{L}(X,Y)$

  • DANIELE PUGLISI (a1)

Abstract

In this paper we investigate the nature of family of pairs of separable Banach spaces (X, Y) such that $\mathcal{K}(X,Y)$ is complemented in $\mathcal{L}(X,Y)$ . It is proved that the family of pairs (X,Y) of separable Banach spaces such that $\mathcal{K}(X,Y)$ is complemented in $\mathcal{L}(X,Y)$ is not Borel, endowed with the Effros–Borel structure.

    • Send article to Kindle

      To send this article to your Kindle, first ensure no-reply@cambridge.org is added to your Approved Personal Document E-mail List under your Personal Document Settings on the Manage Your Content and Devices page of your Amazon account. Then enter the ‘name’ part of your Kindle email address below. Find out more about sending to your Kindle. Find out more about sending to your Kindle.

      Note you can select to send to either the @free.kindle.com or @kindle.com variations. ‘@free.kindle.com’ emails are free but can only be sent to your device when it is connected to wi-fi. ‘@kindle.com’ emails can be delivered even when you are not connected to wi-fi, but note that service fees apply.

      Find out more about the Kindle Personal Document Service.

      THE POSITION OF $\mathcal{K}(X,Y)$ IN $\mathcal{L}(X,Y)$
      Available formats
      ×

      Send article to Dropbox

      To send this article to your Dropbox account, please select one or more formats and confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your <service> account. Find out more about sending content to Dropbox.

      THE POSITION OF $\mathcal{K}(X,Y)$ IN $\mathcal{L}(X,Y)$
      Available formats
      ×

      Send article to Google Drive

      To send this article to your Google Drive account, please select one or more formats and confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your <service> account. Find out more about sending content to Google Drive.

      THE POSITION OF $\mathcal{K}(X,Y)$ IN $\mathcal{L}(X,Y)$
      Available formats
      ×

Copyright

References

Hide All
1.Albiac, F. and Kalton, N. J., Topics in Banach space theory, Graduate Texts in Mathematics, vol 233 (Springer, New York, NY, 2006).
2.Argyros, S. A. and Haydon, R. G., A hereditarily indecomposable $\mathcal{L}_\infty$-space that solves the scalar-plus-compact problem, Acta Math. 206 (1) (2011), 154.
3.Arterburn, D. and Whitley, R. J., Projections in the space of bounded linear operators, Pacific J. Math. 15 (1965), 739746.
4.Bossard, B., A coding of separable Banach spaces. Analytic and coanalytic families of Banach spaces, Fund. Math. 172 (2) (2002), 117152.
5.Bourgain, J., New classes of $\mathcal{L}_p$-spaces, Lecture Notes in Mathematics, vol. 889 (Springer-Verlag, Berlin, Germany, 1981).
6.Bourgain, J. and Delbaen, F., A class of special $\mathcal{L}_\infty$ spaces, Acta Math. 145 (3–4) (1980), 155176.
7.Delpech, S., A short proof of Pitt's compactness theorem, Proc. Amer. Math. Soc. 137 (4) (2009), 13711372.
8.Diestel, J., Geometry of Banach spaces: selected topics, Lecture Notes in Mathematics, vol. 485 (Springer-Verlag, Berlin, Germany, 1975).
9.Dodos, P., Banach spaces and descriptive set theory: selected topics, Lecture Notes in Mathematics, vol. 1993, (Springer-Verlag, Berlin, Germany, 2010).
10.Emmanuele, G., A remark on the containment of c 0 in spaces of compact operators, Math. Proc. Camb. Philos. Soc. 111 (2) (1992), 331335.
11.Emmanuele, G., Answer to a question by M. Feder about $\mathcal{K}(X,Y)$, Rev. Mat. Univ. Complut. Madrid 6 (2) (1993), 263266.
12.Freeman, D., Odell, E. and Schlumprecht, Th., The universality of ℓ1 as a dual space, Math. Ann. 351 (1) (2011), 149186.
13.Kalton, N. J., Spaces of compact operators, Math. Ann. 208 (1974), 267278.
14.Kalton, N. J. and Werner, D., Property (M), M-ideals, and almost isometric structure of Banach spaces, J. Reine Angew. Math. 461 (1995), 137178.
15.Kechris, A. S., Classical descriptive set theory, Graduate Texts in Mathematics, vol. 156 (Springer-Verlag, New York, 1995).
16.Lindenstrauss, J. and Tzafriri, L., Classical Banach spaces, Lecture Notes in Mathematics, vol. 338 (Springer-Verlag, Berlin, Germany, 1973).
17.Pelczynski, A., Universal bases, Studia Math. 32 (1969), 247268.
18.Thorp, E., Projections onto the subspace of compact operators, Pacific J. Math. 10 (1960), 693696.
19.Tong, A. E. and Wilken, D. R., The uncomplemented subspace K(E,F), Studia Math. 37 (1971), 227236.

Keywords

Related content

Powered by UNSILO

THE POSITION OF $\mathcal{K}(X,Y)$ IN $\mathcal{L}(X,Y)$

  • DANIELE PUGLISI (a1)

Metrics

Full text views

Total number of HTML views: 0
Total number of PDF views: 0 *
Loading metrics...

Abstract views

Total abstract views: 0 *
Loading metrics...

* Views captured on Cambridge Core between <date>. This data will be updated every 24 hours.

Usage data cannot currently be displayed.