BOUNDED APPROXIMATION PROPERTIES VIA INTEGRAL AND NUCLEAR OPERATORS

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

来源：Proceedings of the American Mathematical Society, 2010, 138(1): 287-297.

DOI：10.1090/S0002-9939-09-10061-8

• Banach spaces
• Banach operator ideals
• bounded approximation properties

Let X be a Banach space and let A be a Banach operator ideal. We say that X has the lambda-bounded approximation property for A (lambda-BAP for A) if for every Banach space Y and every operator T is an element of A(X, Y), there exists a net (S(alpha)) of finite rank operators on X such that S(alpha) -> I(X) uniformly on compact subsets of X and
lim(alpha) sup parallel to TS(alpha)parallel to(A)<=lambda parallel to T parallel to(A).
We prove that the (classical) lambda-BAP is precisely the lambda-BAP for the ideal I of integral operators, or equivalently, for the ideal SI of strictly integral operators. We also prove that the weak lambda-BAP is precisely the lambda-BAP for the ideal N of nuclear operators.

• 出版日期2010-1