Abstract
We derive a criterion for a Banach space to fail the uniform approximation property (UAP). This criterion is applied to prove that q, spaces of matrices fail UAPifp>80. 0. A Banach space X has the uniform approximation property (abbreviated UAP) if for every integer k there exists an integer m(k) such that for every k-dimensional subspace E of X there exists an operator T : X ~ X such that ][T][~A, rkT<=m(k) and TpE=Id~ for some A < ~ which is independent of k. (TE denotes the restriction of T to E and IdE denotes the identity on E.)
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.
