منابع مشابه
Tensor Products of Closed Operators on Banach Spaces
Let A and B be closed operators on Banach spaces X and Y. Assume that A and B have nonempty resolvent sets and that the spectra of A and B are unbounded. Let 01 be a uniform cross norm on X @ Y. Using the Gelfand theory and resolvent algebra techniques, a spectral mapping theorem is proven for a certain class of rational functions of A and B. The class of admissable rational functions (includin...
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intimately connected with duality theory (the notation is that of [1]). In both cases the middle algebra is the closure of L(G) in the dual of the first algebra and also the predual of the third algebra (at least when G is amenable in the second case). Furthermore, the third algebra is closely connected with the multiplier algebra of the first algebra. For abelian groups, compact or discrete, V...
متن کاملDenting Points in Tensor Products of Banach Spaces
Let dent A denote the set of denting points of a subset A of some Banach space. We prove dent cl co( K ® L) = dent K ® dent L for closed, bounded, absolutely convex subsets K and L of Banach spaces X and Y. Here the closure refers to the completion of X ® Y w.r.t. some reasonable crossnorm.
متن کاملOn The Interpolation of Injective or Projective Tensor Products of Banach Spaces
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...
متن کاملInterpolation of Banach Algebras and Tensor Products of Banach Couples
We consider interpolation of unital Banach algebras, in the special case when the intersection space is non-unital, giving precise conditions of when an interpolation algebra is unital.
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ژورنال
عنوان ژورنال: Kodai Mathematical Journal
سال: 1957
ISSN: 0386-5991
DOI: 10.2996/kmj/1138843934