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On Subspectra Generated in Subalgebras
Author(s) -
Wawrzyńczyk Antoni
Publication year - 2003
Publication title -
bulletin of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 2.396
H-Index - 48
eISSN - 1469-2120
pISSN - 0024-6093
DOI - 10.1112/s002460930200187x
Subject(s) - mathematics , ideal (ethics) , invertible matrix , codimension , commutative property , subalgebra , unital , mathematics subject classification , class (philosophy) , pure mathematics , combinatorics , discrete mathematics , algebra over a field , philosophy , epistemology , artificial intelligence , computer science
Let B be a unital commutative Banach algebra, and let A be an arbitrary subalgebra of B . Suppose that an ideal I ⊂ A consists of elements that are non‐invertible in B . Then there exists an ideal J in A that: (i) contains I , (ii) also consists of elements non‐invertible in B , and (iii) is of codimension one in A . This result is used in the study of a class of subspectra on A . 2000 Mathematics Subject Classification 46J20.