A Class of Reflexive Symmetric Bk-Spaces
1969 ◽
Vol 21
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pp. 602-608
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Keyword(s):
Bk Space
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We denote by ω the linear space of all sequences of real or complex numbers. A linear subspace of ω is called a sequence space. A sequence space E is a BK-space (9) if it is equipped with a norm under which: first, E is a Banach space and second, each of the coordinate maps x → xi is continuous. Let ∑ be the group of all permutations of Z+ = {1, 2, 3, …}. If x ∈ ω and σ ∈ ∑, the sequence xσ is defined by (xσ)i = xσ(i)). A sequence space E is symmetric if xσ ∈ E whenever x ∈ E and σ ∈ ∑. Accounts of symmetric sequence spaces occur in (3; 7; 8).
1967 ◽
Vol 63
(4)
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pp. 997-1019
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Keyword(s):
Keyword(s):
1966 ◽
Vol 18
◽
pp. 1281-1293
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Keyword(s):
1970 ◽
Vol 11
(2)
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pp. 162-166
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Keyword(s):
2002 ◽
Vol 30
(7)
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pp. 383-392
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Keyword(s):
2003 ◽
Vol 10
(1)
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pp. 193-200
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Keyword(s):
Keyword(s):