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The Spectral Theory of Upper Triangular Matrices with Entries in a Banach Algebra
Author(s) -
Barnes Bruce A.
Publication year - 2002
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 - 10.1002/1522-2616(200207)241:1<5::aid-mana5>3.0.co;2-f
Subject(s) - mathematics , triangular matrix , banach algebra , spectrum (functional analysis) , diagonal , unital , pure mathematics , matrix (chemical analysis) , banach space , algebra over a field , combinatorics , geometry , physics , quantum mechanics , invertible matrix , materials science , composite material
Assume that T is an upper triangular square matrix with entries in a unital Banach algebra. The main question studied here is: Under what conditions on the entries in T is it true that the spectrum of T is the union of the spectra of the diagonal entries of T ? Also some results are proved concerning the Fredholm theroy of matrices with operator entries.