We present a short and simple proof of the recent result of Yang and Wang [12]. Stimulated by their idea, two geometric parameters Uax（ε） and βx （ε）, both related to Gao＇s modulus of U-convexity of a Banach sp...We present a short and simple proof of the recent result of Yang and Wang [12]. Stimulated by their idea, two geometric parameters Uax（ε） and βx （ε）, both related to Gao＇s modulus of U-convexity of a Banach space X, are introduced. Their properties and the relationships with normal structure are studied. Some existing results involving normal structure and fixed points for non-expansive mappings in Banach spaces are improved.展开更多
1 Notation and Terminology Throughout this note κ is always a regular uncountable cardinal, and λ≥κ acardinal. When we say an ideal I on P_κλ, it means that I is a κ-completenon-principal fine ideal on P_κλ. ...1 Notation and Terminology Throughout this note κ is always a regular uncountable cardinal, and λ≥κ acardinal. When we say an ideal I on P_κλ, it means that I is a κ-completenon-principal fine ideal on P_κλ. If M is a ground model of ZFC, then Ult_U(M)denotes the ultrapower of M associated with U, an ultrapower on P_κλ. Let I be an ideal on P_κλ. We consider the generic extension of M given by thecompletion of Boolean algebra P(P_κλ)/I, i.e. forcing with【R(I),≤_I), where R(I)展开更多
文摘We present a short and simple proof of the recent result of Yang and Wang [12]. Stimulated by their idea, two geometric parameters Uax（ε） and βx （ε）, both related to Gao＇s modulus of U-convexity of a Banach space X, are introduced. Their properties and the relationships with normal structure are studied. Some existing results involving normal structure and fixed points for non-expansive mappings in Banach spaces are improved.
文摘1 Notation and Terminology Throughout this note κ is always a regular uncountable cardinal, and λ≥κ acardinal. When we say an ideal I on P_κλ, it means that I is a κ-completenon-principal fine ideal on P_κλ. If M is a ground model of ZFC, then Ult_U(M)denotes the ultrapower of M associated with U, an ultrapower on P_κλ. Let I be an ideal on P_κλ. We consider the generic extension of M given by thecompletion of Boolean algebra P(P_κλ)/I, i.e. forcing with【R(I),≤_I), where R(I)
