[PDF][PDF] Applications of the scarcity theorem in ordered Banach algebras
S Mouton - Studia Mathematica, 2014 - pdfs.semanticscholar.org
Studia Mathematica, 2014•pdfs.semanticscholar.org
… If a function f is analytic on a domain D in the complex plane and with values in a Banach
algebra, then either the subset of D on which the spectrum of f is finite is “very small” in
some sense, or it is the whole of D, in which case the spectrum of f is even uniformly finite
on D. … Let A be an ordered Banach algebra with certain natural properties and let a and b
be positive elements in A such that b dominates a. If b is in the radical of A, then so is a. …
Let f : D → A be analytic, where D is a domain in C and A is a Banach algebra. Then either …
algebra, then either the subset of D on which the spectrum of f is finite is “very small” in
some sense, or it is the whole of D, in which case the spectrum of f is even uniformly finite
on D. … Let A be an ordered Banach algebra with certain natural properties and let a and b
be positive elements in A such that b dominates a. If b is in the radical of A, then so is a. …
Let f : D → A be analytic, where D is a domain in C and A is a Banach algebra. Then either …
If a function f is analytic on a domain D in the complex plane and with values in a Banach algebra, then either the subset of D on which the spectrum of f is finite is “very small” in some sense, or it is the whole of D, in which case the spectrum of f is even uniformly finite on D.
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