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Symmetric Sequence Subspaces of C (α)
Author(s) -
Leung Denny H.
Publication year - 1999
Publication title -
journal of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.441
H-Index - 62
eISSN - 1469-7750
pISSN - 0024-6107
DOI - 10.1112/s0024610799007218
Subject(s) - hausdorff space , sequence (biology) , linear subspace , mathematics , banach space , countable set , mathematical proof , sequence space , pure mathematics , space (punctuation) , function space , discrete mathematics , computer science , geometry , genetics , biology , operating system
Two main results are shown: (1) a characterisation of the symmetric sequence spaces which embed into C (ω ω ), and (2) a characterisation, in terms of the Orlicz function M , of the Orlicz sequence spaces h M which embed into C ( K ) for some countable compact Hausdorff space K . The proofs make use of the Schreier families of sets, which have found wide applications in Banach space theory.