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- 저자 : Christopher Boyd (검색결과 2 건)
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HOLOMORPHIC FUNCTIONS AND THE BB-PROPERTY ON PRODUCT SPACES
Boyd, Christopher Korean Mathematical Society 2004 대한수학회지 Vol.41 No.1
In [25] Taskinen shows that if $\{E_n\}_n\;and\;\{F_n\}_n$ are two sequences of Frechet spaces such that ($E_m,\;F_n$) has the BB-property for all m and n then (${\Pi}_m\;E_m,\;{\Pi}_n\;F_n$) also has the ΒΒ-property. Here we investigate when this result extends to (i) arbitrary products of Frechet spaces, (ii) countable products of DFN spaces, (iii) countable direct sums of Frechet nuclear spaces. We also look at topologies properties of ($H(U),\;\tau$) for U balanced open in a product of Frechet spaces and $\tau\;=\;{\tau}_o,\;{\tau}_{\omega}\;or\;{\tau}_{\delta}$.
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Holomorphic functions and the BB-property on product spaces
Christopher Boyd 대한수학회 2004 대한수학회지 Vol.41 No.1
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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