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On Certain Densely Invariant Quantities of Linear Operators
Author(s) -
Cross R. W.
Publication year - 1996
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.19961780105
Subject(s) - mathematics , linear subspace , invariant (physics) , pure mathematics , operator (biology) , linear map , property (philosophy) , combinatorics , discrete mathematics , mathematical physics , biochemistry , chemistry , repressor , transcription factor , gene , philosophy , epistemology
Let L ( X,Y ) denote the class of linear transformations T:D ( T ) ⊂ X → Y where X and Y are normed spaces. A quantity f is called densely invariant if for every system L ( X, Y ) and every operator T ϵ L ( X,Y ) we have f ( T/E ) = f ( T ) whenever E is a core of T . The density invariance of certain well known quantities is established. In case Y is complete and T is closable, a stronger property is shown to hold for some of these quantitites, namely invariance under restriction to dense subspaces.