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Search: MSC category 46M05 ( Tensor products [See also 46A32, 46B28, 47A80] )

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1. CMB 2010 (vol 53 pp. 690)

Puerta, M. E.; Loaiza, G.
On the Maximal Operator Ideal Associated with a Tensor Norm Defined by Interpolation Spaces
The classical approach to studying operator ideals using tensor norms mainly focuses on those tensor norms and operator ideals defined by means of $\ell_p$ spaces. In a previous paper, an interpolation space, defined via the real method and using $\ell_p$ spaces, was used to define a tensor norm, and the associated minimal operator ideals were characterized. In this paper, the next natural step is taken, that is, the corresponding maximal operator ideals are characterized. As an application, necessary and sufficient conditions for the coincidence of the maximal and minimal ideals are given. Finally, the previous results are used in order to find some new metric properties of the mentioned tensor norm.

Keywords:maximal operator ideals, ultraproducts of spaces, interpolation spaces
Categories:46M05, 46M35, 46A32

2. CMB 2000 (vol 43 pp. 138)

Boyd, C.
Exponential Laws for the Nachbin Ported Topology
We show that for $U$ and $V$ balanced open subsets of (Qno) Fr\'echet spaces $E$ and $F$ that we have the topological identity $$ \bigl( {\cal H}(U\times V), \tau_\omega \bigr) = \biggl( {\cal H} \Bigl( U; \bigl( {\cal H}(V), \tau_\omega \bigr) \Bigr), \tau_\omega \biggr). $$ Analogous results for the compact open topology have long been established. We also give an example to show that the (Qno) hypothesis on both $E$ and $F$ is necessary.

Categories:46G20, 18D15, 46M05

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