منابع مشابه
p-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...
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We prove a general result on the factorization of matrix-valued analytic functions. We deduce that if (E0, E1) and (F0, F1) are interpolation pairs with dense intersections, then under some conditions on the spaces E0, E1, F0 and F1, we have [E0⊗̂F0, E1⊗̂F1]θ = [E0, E1]θ⊗̂[F0, F1]θ, 0 < θ < 1. We find also conditions on the spaces E0, E1, F0 and F1 , so that the following holds [E0 ∨ ⊗F0, E1 ∨ ⊗F1...
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In this article, we proved the following results. Let L(F (ni)) be the free group factor on ni generators and λ(gi) be one of standard generators of L(F (ni)) for 1 ≤ i ≤ N . Let Ai be the abelian von Neumann subalgebra of L(F (ni)) generated by λ(gi). Then the abelian von Neumann subalgebra ⊗i=1Ai is a maximal injective von Neumann subalgebra of ⊗i=1L(F (ni)). When N is equal to infinity, we o...
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We classify all continuous tensor product systems of Hilbert spaces which are “infinitely divisible” in the sense that they have an associated logarithmic structure. These results are applied to the theory of E0-semigroups to deduce that every E0-semigroup possessing sufficiently many “decomposable” operators must be cocycle conjugate to a CCR flow. A path space is an abstraction of the set of ...
متن کاملSeparably Injective Banach Spaces
It is no exaggeration to say that the theory of separably injective spaces is quite different from that of injective spaces. In this chapter we will explain why. Indeed, we will enter now in the main topic of the monograph, namely, separably injective spaces and their “universal” version. After giving the main definitions and taking a look at the first natural examples one encounters, we presen...
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ژورنال
عنوان ژورنال: Studia Mathematica
سال: 2019
ISSN: 0039-3223,1730-6337
DOI: 10.4064/sm170601-11-12