NEW EXAMPLES OF c 0 - SATURATED BANACH
نویسنده
چکیده
For every p ∈ (1, ∞), an isomorphically polyhedral Banach space Ep is constructed which has an unconditional basis and does not embed isomorphically into a C(K) space for any countable and compact metric space K. Moreover, Ep admits a quotient isomorphic to ℓp.
منابع مشابه
NEW EXAMPLES OF c 0 - SATURATED BANACH SPACES II
For every Banach space Z with a shrinking unconditional basis satisfying an upper p-estimate for some p > 1, an isomorphically polyhedral Banach space is constructed which has an unconditional basis and admits a quotient isomorphic to Z. It follows that reflexive Banach spaces with an unconditional basis and non-trivial type, Tsirelson's original space and (P c0) ℓp for p ∈ (1, ∞), are isomorph...
متن کاملOn Unconditionally Saturated Banach Spaces
We prove a structural property of the class of unconditionally saturated separable Banach spaces. We show, in particular, that for every analytic set A, in the Effros-Borel space of subspaces of C[0, 1], of unconditionally saturated separable Banach spaces, there exists an unconditionally saturated Banach space Y , with a Schauder basis, that contains isomorphic copies of every space X in the c...
متن کاملSome stability properties of c 0 - saturated spaces Denny
A Banach space is c0-saturated if all of its closed infinite dimensional subspaces contain an isomorph of c0. In this article, we study the stability of this property under the formation of direct sums and tensor products. Some of the results are: (1) a slightly more general version of the fact that c0-sums of c0saturated spaces are c0-saturated; (2) C(K,E) is c0-saturated if both C(K) and E ar...
متن کاملA note on Banach spaces with l1-saturated duals
Let E and F be Banach spaces. We say that E is F -saturated if every infinite dimensional closed subspace of E contains an isomorphic copy of F . In [2], it is shown that there exists a c0-saturated Banach space with an unconditional basis whose dual contains an isomorphic copy of l2. In this note, we give an example where the dual situation occurs. It is shown that there is a Banach space with...
متن کامل$(-1)$-Weak Amenability of Second Dual of Real Banach Algebras
Let $ (A,| cdot |) $ be a real Banach algebra, a complex algebra $ A_mathbb{C} $ be a complexification of $ A $ and $ | | cdot | | $ be an algebra norm on $ A_mathbb{C} $ satisfying a simple condition together with the norm $ | cdot | $ on $ A$. In this paper we first show that $ A^* $ is a real Banach $ A^{**}$-module if and only if $ (A_mathbb{C})^* $ is a complex Banach $ (A_mathbb{C})^{...
متن کامل