Abstract
It is established by an example that the distance of a bounded linear operatorS from the class of compact operators on a Banach space is not always uniformly comparable with that of its adjointS′. This provides a negative solution to an old problem. It is also shown that the seminorms due to Schechter and Weis, that measure the deviation from strict singularity or strict cosingularity of an operator, are not uniformly comparable with the corresponding distance functions. Both results rely on a general construction related to certain approximation properties that are associated with closed ideals of operators.
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
