Covering a compact set in a Banach space by an operator range of a Banach space with basis Academic Article uri icon

abstract

  • A Banach space X has the approximation property if and only if every compact set in X is in the range of a one-to-one bounded linear operator from a space that has a Schauder basis. Characterizations are given for ℒ p spaces and quotients of ℒ p spaces in terms of covering compact sets in X by operator ranges from ℒ p spaces. A Banach space X is a ℒ 1 space if and only if every compact set in X is contained in the closed convex symmetric hull of a basic sequence which converges to zero.

author list (cited authors)

  • Fonf, V. P., Johnson, W. B., Plichko, A. M., & Shevchyk, V. V.

citation count

  • 1

complete list of authors

  • Fonf, VP||Johnson, WB||Plichko, AM||Shevchyk, VV

publication date

  • September 2005