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Nuclear Cyclic Diagonal Mappings
Author(s) -
Kaiser R. J.,
Retherford J. R.
Publication year - 1984
Publication title -
mathematische nachrichten
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.913
H-Index - 50
eISSN - 1522-2616
pISSN - 0025-584X
DOI - 10.1002/mana.19841190111
Subject(s) - mathematics , sequence (biology) , schauder basis , banach space , diagonal , pure mathematics , basis (linear algebra) , sequence space , simple (philosophy) , space (punctuation) , eigenvalues and eigenvectors , sign (mathematics) , operator (biology) , mathematical analysis , geometry , philosophy , linguistics , genetics , physics , biochemistry , epistemology , repressor , quantum mechanics , chemistry , gene , transcription factor , biology
In this note we construct nuclear operators whose eigenvalues are preassigned up to change of sign (or the n th roots of unity in the general case). These operators have a remarkably simple structure and in a special case yield a “natural” way of obtaining the modular sequence spaces of H. Rosenthal. Recall that a (Schauder) basis for a Banach space X is a sequence ( x n ) in X such that for every x ε X there is a unique sequence of scalars ( a n ) such thatconvergence in the topology of X . If X is a Banach space with a basis ( x n ) we can identify X with a sequence space by the correspondence.