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On Strong Spectrally Bounded LMC*‐Algebras
Author(s) -
Fragoulopoulou Maria
Publication year - 1987
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.19871340122
Subject(s) - mathematics , bounded function , subalgebra , hilbert space , algebra over a field , regular polygon , pure mathematics , banach algebra , representation (politics) , space (punctuation) , mathematical analysis , geometry , linguistics , philosophy , politics , political science , law
A locally m ‐convex algebra E ≡ ( E , ( p α ); α ∈ A ) is called “strong spectrally bounded” if supp α ( x ) < ∞, for every x ∈ E. A locally m ‐convex C *‐algebra of the last kind always accepts a faithful representation, say φ, with a continuous inverse, such that ‖‖φ( x )‖‖ = supp α , for al x ∈ E . Particularly, in case E is moreover barrelled, φ is also continuous, E becoming thus a *‐subalgebra of a concrete C *‐algebra ℒ( H ), H a Hilbert space.