منابع مشابه
Definable norms and definable types over Banach spaces
A central question in Banach space theory has been to identify the class of Banach spaces that contain almost isometric copies of the classical sequence spaces `p and c0. Banach space theory entered a new era in the mid 1970’s, when B. Tsirelson [34] constructed the first space not containing isomorphic copies any of the classical sequence spaces. Tsirelson’s space has been called “the first tr...
متن کاملDouble-dual n-types over Banach spaces not containing ℓ1
Let E be a Banach space. The concept of n-type over E is introduced here, generalizing the concept of type over E introduced by Krivine and Maurey. Let E′′ be the second dual of E and fix g′′ 1 , . . . ,g′′ n ∈ E′′. The function τ : E×Rn → R, defined by letting τ(x,a1, . . . ,an) = ‖x+∑ni=1aig′′ i ‖ for all x ∈ E and all a1, . . . ,an ∈R, defines an n-type over E. Types that can be represented ...
متن کاملDOUBLE - DUAL n - TYPES OVER BANACH SPACES NOT CONTAINING
Let E be a Banach space. The concept of n-type over E is introduced here, generalizing the concept of type over E introduced by Krivine and Maurey. Let E′′ be the second dual of E and fix g′′ 1 , . . . ,g′′ n ∈ E′′. The function τ : E×Rn → R, defined by letting τ(x,a1, . . . ,an) = ‖x+∑ni=1aig′′ i ‖ for all x ∈ E and all a1, . . . ,an ∈R, defines an n-type over E. Types that can be represented ...
متن کاملTypes on stable Banach spaces
We prove a geometric characterization of Banach space stability. We show that a Banach space X is stable if and only if the following condition holds. Whenever X̂ is an ultrapower of X and B is a ball in X̂, the intersection B ∩X can be uniformly approximated by finite unions and intersections of balls in X; furthermore, the radius of these balls can be taken arbitrarily close to the radius of B,...
متن کاملBanach Spaces as Data Types
We introduce the operators modified limit and accumulation on a Banach space, and we use this to define what we mean by being internally computable over the space. We prove that any externally computable function from a computable metric space to a computable Banach space is internally computable. We motivate the need for internal concepts of computability by observing that the complexity of th...
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ژورنال
عنوان ژورنال: Notre Dame Journal of Formal Logic
سال: 2005
ISSN: 0029-4527
DOI: 10.1305/ndjfl/1107220672