# Wydawnictwa / Czasopisma IMPAN / Studia Mathematica / Wszystkie zeszyty

## Some duality results on bounded approximation properties of pairs

### Tom 217 / 2013

Studia Mathematica 217 (2013), 79-94 MSC: Primary 46B28; Secondary 46B20, 46B10, 47B10. DOI: 10.4064/sm217-1-5

#### Streszczenie

The main result is as follows. Let $X$ be a Banach space and let $Y$ be a closed subspace of $X$. Assume that the pair $(X^{*}, Y^{\perp })$ has the $\lambda$-bounded approximation property. Then there exists a net $( S_\alpha )$ of finite-rank operators on $X$ such that $S_\alpha (Y) \subset Y$ and $\| S_\alpha \| \leq \lambda$ for all $\alpha$, and $( S_\alpha )$ and $( S^{*}_\alpha )$ converge pointwise to the identity operators on $X$ and $X^{*}$, respectively. This means that the pair $(X,Y)$ has the $\lambda$-bounded duality approximation property.

#### Autorzy

• Eve OjaFaculty of Mathematics
and Computer Science
Tartu University
J. Liivi 2
50409 Tartu, Estonia
and
Kohtu 6
10130 Tallinn, Estonia
e-mail
• Silja TreialtFaculty of Mathematics and Computer Science
Tartu University
J. Liivi 2
50409 Tartu, Estonia
e-mail

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