A unified approach to approximation properties and ideals

作者：Kim Ju Myung^*; Lee Keun Young

来源：Studia Mathematica, 2017, 238(3): 249-269.

DOI：10.4064/sm8709-1-2017

• metric approximation property
• weak metric approximation property
• approximation property
• ideal
• space of operators

We use a unified argument to obtain relationships between approximation properties and ideals in spaces of some operators. We prove that a Banach space X (respectively, the dual space X-* of X) has the metric approximation property if and only if for every Banach space Y and every operator T from Y to X (respectively, T from X to Y), there exists a
phi is an element of HB(F(X)T, span(F(X)T boolean OR {T}))
(respectively, phi is an element of HB(TF(X), span(TF(X) boolean OR {T})))
such that
phi(x(*) circle times y)(R) = x(*) (Ry) (respectively, phi(x(**) circle times y(*))(R) = x(**) (R-a y(*)))
for every x(*) is an element of X-* and y E Y (respectively, x(**) is an element of X-** and y(*) is an element of Y-*), and every R is an element of span(F(X)T boolean OR {T}) (respectively, R is an element of span(TF(X) boolean OR {T})).

• 出版日期2017