Journal of Operator Theory

Volume 94, Issue 1, Summer 2025 pp. 3-21.

Representation of compact operators between Banach spaces

Authors: G. Ramesh (1), M. Veena Sangeetha (2), Shanola S. Sequeira (3)
Author institution: (1) Department of Mathematics, IIT Hyderabad, Sangareddy, Telangana, 502284, India
(2) Department of Mathematics, IIT Hyderabad, Sangareddy, Telangana, 502284, India and, current address, Department of Mathematics and Statistics, GITAM School of Science, Hyderabad, Telangana 502329, India
(3) Department of Mathematics, IIT Hyderabad, Sangareddy, Telangana, 502284, India and Department of Mathematics and Statistics, IIT Kanpur, Uttar Pradesh, 208016, India

Summary: In this article, we give a representation for compact operators acting between reflexive Banach spaces, which generalizes the representation given by Edmunds et al. for compact operators between reflexive Banach spaces with strictly convex duals. Further, we give a representation for a class of operators on Banach spaces, that is comparable to the classical spectral representation for compact normal operators on Hilbert spaces. Finally, we give an example to illustrate our main result.

DOI: http://dx.doi.org/10.7900/jot.2023aug07.2469
Keywords: Banach space, compact operator, norm attaining operator, spectral theorem

Contents Full-Text PDF