Uniform non-\(\ell_1^n\)-ness of \(\ell_1\)-sums of Banach spaces

• Autorzy: Mikio Kato , Takayuki Tamura
• Języki publikacji: EN

Abstrakty

EN

We shall characterize the uniform non-\(\ell_1^n\)-ness of the \(\ell_1\)-sum \((X_1 \oplus\dots\oplus X_m)_1\) of a finite number of Banach spaces \(X_1 ,\dots, X_m\). Also we shall obtain that \((X_1 \oplus \dots \oplus X_m)_1\) is uniformly non-\(\ell_1^{m+1}\) if and only if all \(X_1 ,\dots , X_m\) are uniformly non-square (note that \((X_1 \oplus \dots \oplus X_m)_1\) is not uniformly non-\(\ell_1^m\)). Several related results will be presented.

Słowa kluczowe

EN

\(\ell_1\)-sum of Banach spaces; uniformly non-square space; uniformly non-\(\ell_1^n\)-space; super-reflexivity; fixed point property

• Wydawca: Polish Mathematical Society
• Czasopismo: Commentationes Mathematicae
• Rocznik: 2007
• Tom: 47
• Numer: 2

Daty

wydano

2007

online

2017-12-19

Twórcy

autor

Mikio Kato

autor

Takayuki Tamura

Identyfikatory

DOI

10.14708/cm.v47i2.5246