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Spectral Collapse
Author(s) -
Rowell James W.
Publication year - 1986
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/jlms/s2-34.3.479
Subject(s) - subalgebra , mathematics , closure (psychology) , lattice (music) , inverse , banach algebra , pure mathematics , algebra over a field , unital , hull , connection (principal bundle) , banach space , geometry , physics , geology , political science , acoustics , law , oceanography
Following recent work of B . Barnes, we explore various conditions which guarantee inverse closure of a closed subalgebra of a unital Banach algebra. Noting the connection between inverse closure and collapse of the spectral lattice, we then salvage the hull‐boundary relations which remain when the given subalgebra is not necessarily inverse closed. The results of the paper are then applied to determine the extent of spectral collapse in the special case of seminormal elements of a B ∗ ‐algebra.