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Holomorphic functions and the BB-property on product spaces

Christopher Boyd
대한수학회 (The Korean Mathematical Society)|2004.01|대한수학회지 (Journal of the KMS)|제41권 제1호|pp. 39-50

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Abstract

In [25] Taskinen shows that if {En}n and {Fn}n are two sequences of Fr´echet spaces such that (Em, Fn) has the BBproperty for all m and n then m Em,n Fn also has the BBproperty. Here we investigate when this result extends to (i) arbitrary products of Fr´echet spaces, (ii) countable products of DFN spaces, (iii) countable direct sums of Fr´echet nuclear spaces. We also look at topologies properties of (H(U), τ) for U balanced open in a product of Fr´echet spaces and τ = τo, τω or τδ.

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