BOUNDED APPROXIMATION PROPERTIES IN TERMS OF C[0,1]

作者：Lima Asvald^*; Lima Vegard; Oja Eve

来源：Mathematica Scandinavica, 2012, 110(1): 45-58.

Let X be a Banach space and let J be the Banach operator ideal of integral operators. We prove that X has the lambda-bounded approximation property (lambda-BAP) if and only if for every operator T is an element of J(X, C[0, 1]*) there exists a net (S-alpha) of finite-rank operators on X such that S-alpha -%26gt; I-X pointwise and %26lt;br%26gt;lim(alpha) sup parallel to TS alpha parallel to(J) %26lt;= lambda parallel to T parallel to(J). %26lt;br%26gt;We also prove that replacing J by the ideal N of nuclear operators yields a condition which is equivalent to the weak lambda-BAP.

• 出版日期2012