On injective tensor powers of ℓ1
نویسندگان
چکیده
In this paper we prove that the 3-fold injective tensor product ℓ1⊗ˆεℓ1⊗ˆεℓ1 is not isomorphic to any subspace of ℓ1⊗ˆεℓ1. This result provides a new solution problem Diestel on projective products c0. Moreover, implies for infinite countable compact metric space K, C(K)⊗ˆπC(K)⊗ˆπC(K) quotient C(K)⊗ˆπC(K).
منابع مشابه
A remark on asymptotic enumeration of highest weights in tensor powers of a representation
We consider the semigroup $S$ of highest weights appearing in tensor powers $V^{otimes k}$ of a finite dimensional representation $V$ of a connected reductive group. We describe the cone generated by $S$ as the cone over the weight polytope of $V$ intersected with the positive Weyl chamber. From this we get a description for the asymptotic of the number of highest weights appearing in $V^{otime...
متن کاملOn Tensor Powers of Integer Programs
We de ne a natural product on integer programming problems with nonnegative coe cients. Hypergraph covering problems are a special case of such integer programs, and the product we de ne is a generalization of the usual hypergraph product. The main theorem of this paper gives a su cient condition under which the solution to the nth power of an integer program is asymptotically as good as the so...
متن کاملp-Summing Operators on Injective Tensor Products of Spaces
Let X, Y and Z be Banach spaces, and let ∏ p(Y, Z) (1 ≤ p < ∞) denote the space of p-summing operators from Y to Z. We show that, if X is a £∞-space, then a bounded linear operator T : X⊗̂ǫY −→ Z is 1-summing if and only if a naturally associated operator T : X −→ ∏ 1(Y, Z) is 1-summing. This result need not be true if X is not a £∞-space. For p > 1, several examples are given with X = C[0, 1] t...
متن کاملDeissler Rank Complexity of Powers of Indecomposable Injective Modules
Minimality ranks in the style of Deissler are one way of measuring the structural complexity of minimal extensions of first-order structures. In particular, positive Deissler rank measures the complexity of the injective envelope of a module as an extension of that module. In this paper we solve a problem of the second author by showing that certain injective envelopes have the maximum possible...
متن کاملValuations on Tensor Powers of a Division Algebra
We study the following question in this paper: If p is a prime, m a positive integer, and S = (sm, . . . , s1) an arbitrary sequence consisting of “Y ”or “N”, does there exist a division algebra of exponent p over a valued field (F, v) such that the underlying division algebra of the tensor power D⊗p i has a valuation extending v if and only if sm−i = Y ? We show that if such an algebra exists,...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Journal of Mathematical Analysis and Applications
سال: 2021
ISSN: ['0022-247X', '1096-0813']
DOI: https://doi.org/10.1016/j.jmaa.2020.124581