A NON-SEPARABLE REFLEXIVE BANACH SPACE ON WHICH THERE ARE FEW OPERATORS

H. M. WARK

doi:10.1112/S0024610701002393

Abstract

It is shown that there exists a non-separable reflexive Banach space on which every bounded linear operator is the sum of a scalar multiple of the identity operator and an operator of separable range. There is a strong sense that such a Banach space has as few operators as its linear and topological properties allow.

Crossref Citations

This article has been cited by the following publications. This list is generated based on data provided by Crossref.

Plebanek, Grzegorz 2004. A construction of a Banach space C(K) with few operators. Topology and its Applications, Vol. 143, Issue. 1-3, p. 217.

Argyros, S.A. Lopez-Abad, J. and Todorcevic, S. 2005. A class of Banach spaces with few non-strictly singular operators. Journal of Functional Analysis, Vol. 222, Issue. 2, p. 306.

Koszmider, P. 2005. Projections in Weakly Compactly Generated Banach Spaces and Chang's Conjecture. Journal of Applied Analysis, Vol. 11, Issue. 2,

Koszmider, Piotr 2005. On decompositions of Banach spaces of continuous functions on Mrówka’s spaces. Proceedings of the American Mathematical Society, Vol. 133, Issue. 7, p. 2137.

Cheng, Li Xin and Zhong, Huai Jie 2006. On Hereditarily Indecomposable Banach Spaces. Acta Mathematica Sinica, English Series, Vol. 22, Issue. 3, p. 751.

Todorcevic, Stevo 2010. Handbook of Set Theory. p. 215.

Koszmider, Piotr and Zieliński, Przemysław 2011. Complementation and decompositions in some weakly Lindelöf Banach spaces. Journal of Mathematical Analysis and Applications, Vol. 376, Issue. 1, p. 329.

Kania, Tomasz Koszmider, Piotr and Laustsen, Niels Jakob 2015. Banach spaces whose algebra of bounded operators has the integers as their K0-group. Journal of Mathematical Analysis and Applications, Vol. 428, Issue. 1, p. 282.

Guirao, Antonio J. Montesinos, Vicente and Zizler, Václav 2016. Open Problems in the Geometry and Analysis of Banach Spaces. p. 1.

Koszmider, Piotr 2018. Uncountable equilateral sets in Banach spaces of the form C(K). Israel Journal of Mathematics, Vol. 224, Issue. 1, p. 83.

Koszmider, Piotr and Laustsen, Niels Jakob 2021. A Banach space induced by an almost disjoint family, admitting only few operators and decompositions. Advances in Mathematics, Vol. 381, Issue. , p. 107613.

Koszmider, Piotr and Ryduchowski, Kamil 2023. Equilateral and separated sets in some Hilbert generated Banach spaces. Proceedings of the American Mathematical Society,

Article contents

A NON-SEPARABLE REFLEXIVE BANACH SPACE ON WHICH THERE ARE FEW OPERATORS

Abstract

Access options

This article has been cited by the following publications. This list is generated based on data provided by Crossref.

Article contents

A NON-SEPARABLE REFLEXIVE BANACH SPACE ON WHICH THERE ARE FEW OPERATORS

Abstract

Access options

Save article to Kindle

Save article to Dropbox

Save article to Google Drive

Reply to: Submit a response

Your details

You have entered the maximum number of contributors

Conflicting interests