Generalized Numerical Index of Function Algebras
Keyword(s):
Let X be a complex Banach space and Cb(Ω:X) be the Banach space of all bounded continuous functions from a Hausdorff space Ω to X, equipped with sup norm. A closed subspace A of Cb(Ω:X) is said to be an X-valued function algebra if it satisfies the following three conditions: (i) A≔{x⁎∘f:f∈A, x⁎∈X⁎} is a closed subalgebra of Cb(Ω), the Banach space of all bounded complex-valued continuous functions; (ii) ϕ⊗x∈A for all ϕ∈A and x∈X; and (iii) ϕf∈A for every ϕ∈A and for every f∈A. It is shown that k-homogeneous polynomial and analytic numerical index of certain X-valued function algebras are the same as those of X.
1969 ◽
Vol 21
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pp. 912-914
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Keyword(s):
1986 ◽
Vol 99
(2)
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pp. 273-283
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1975 ◽
Vol 18
(1)
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pp. 61-65
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Keyword(s):
1978 ◽
Vol 84
(2)
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pp. 323-336
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1989 ◽
Vol 39
(3)
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pp. 353-359
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1978 ◽
Vol 30
(03)
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pp. 490-498
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1969 ◽
Vol 3
(2)
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pp. 137-146
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1960 ◽
Vol 12
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pp. 353-362
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