Properties <inline-formula> <graphic file="1687-1812-2010-342691-i1.gif"/></inline-formula> and <inline-formula> <graphic file="1687-1812-2010-342691-i2.gif"/></inline-formula>, <inline-formula> <graphic file="1687-1812-2010-342691-i3.gif"/></inline-formula> Embeddings in Banach Spaces with 1-Unconditional Basis and <inline-formula> <graphic file="1687-1812-2010-342691-i4.gif"/></inline-formula>

• Main Authors: Fetter Helga, Gamboa de Buen Berta
• Format: Article
• Language: English
• Published: SpringerOpen 2010-01-01
• Series: Fixed Point Theory and Applications
• Online Access: http://www.fixedpointtheoryandapplications.com/content/2010/342691

<p/> <p>We will use Garc&#237;a-Falset and Llor&#233;ns Fuster's paper on the AMC-property to prove that a Banach space <inline-formula> <graphic file="1687-1812-2010-342691-i5.gif"/></inline-formula> that <inline-formula> <graphic file="1687-1812-2010-342691-i6.gif"/></inline-formula> embeds in a subspace <inline-formula> <graphic file="1687-1812-2010-342691-i7.gif"/></inline-formula> of a Banach space <inline-formula> <graphic file="1687-1812-2010-342691-i8.gif"/></inline-formula> with a 1-unconditional basis has the property AMC and thus the weak fixed point property. We will apply this to some results by Cowell and Kalton to prove that every reflexive real Banach space with the property <inline-formula> <graphic file="1687-1812-2010-342691-i9.gif"/></inline-formula> and its dual have the <inline-formula> <graphic file="1687-1812-2010-342691-i10.gif"/></inline-formula> and that a real Banach space <inline-formula> <graphic file="1687-1812-2010-342691-i11.gif"/></inline-formula> such that <inline-formula> <graphic file="1687-1812-2010-342691-i12.gif"/></inline-formula> is <inline-formula> <graphic file="1687-1812-2010-342691-i13.gif"/></inline-formula> sequentially compact and <inline-formula> <graphic file="1687-1812-2010-342691-i14.gif"/></inline-formula> has <inline-formula> <graphic file="1687-1812-2010-342691-i15.gif"/></inline-formula> has the <inline-formula> <graphic file="1687-1812-2010-342691-i16.gif"/></inline-formula>.</p>