On the boundary spectrum in banach algebras Page 1 BULL. AUSTRAL. MATH. SOC.
46HO5, 46H10, 47A10, 06F25 VOL. 74 (2006) [239-246] ON THE BOUNDARY SPECTRUM …

We recall the definition and properties of an algebra cone C of a complex unital Banach
algebra A. It can be shown that C induces on A an ordering which is compatible with the …

Spectral theory in ordered Banach algebras | SpringerLink Skip to main content Advertisement
SpringerLink Log in Menu Find a journal Publish with us Search Cart 1.Home 2.Positivity …

Spectral theory in ordered Banach algebras (OBAs) has been investigated and several
authors have made contributions. However, the results are not applicable to non …

We recall the definition and properties of an algebra cone in an ordered Banach algebra
(OBA) and continue to develop spectral theory for the positive elements. An element a of a …

Let $ a $ be an element of a Banach algebra $ A $. We introduce a compact subset $ T (a) $
of the complex plane, show that the function which maps $ a $ onto $ T (a) $ is upper …

Let x be a positive element of an ordered Banach algebra. We prove a relationship between
the spectra of x and of certain positive elements y for which either xy≤ yx or yx≤ xy …

Let A be a complex unital Banach algebra. An algebra cone in A is a non-empty subset C of
A containing the unit of A and which is closed under addition, multiplication and non …

Let A be a complex Banach algebra with unit 1. A subset C of A is called a cone if C+ C⊆ C
and λC⊆ C for all scalars λ≥ 0. If C satisfies the additional properties that CC⊆ C and 1∈ …

The following problem in an OBA (ordered Banach algebra) has been studied by various
authors: If a and b are positive elements in an OBA such that 0= a= b and if b has a certain …