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On a formula of le Merdy for the complex interpolation of tensor products. (English) Zbl 1216.46020
Summary: C. Le Merdy [Proc. Am. Math. Soc. 126, No. 3, 715–719 (1998; Zbl 0890.47029)] proved the following complex interpolation formula for injective tensor products: [ 2 ˜ ϵ 1 , 2 ˜ ϵ ] 1 2 =S 4 . We investigate whether related formulas hold when considering arbitrary 0<θ<1 instead of 1 2, and give a partially positive answer for θ<1 2 and a negative answer for θ>1 2. Furthermore, we briefly discuss the more general case when 2 is replaced by q , 1<q<2, and 1 and by p 0 and p 1 , respectively.
MSC:
46B70Interpolation between normed linear spaces
46M35Abstract interpolation of topological linear spaces
47B06Riesz operators; eigenvalue distributions; approximation numbers, s-numbers etc.of operators
47B10Operators belonging to operator ideals
46B28Spaces of operators; tensor products; approximation properties