Spectral Characterization of Algebraic Elements | Zendy

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Spectral Characterization of Algebraic Elements

Author(s) -

Ransford Thomas,

White Michael

Publication year - 2001

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/blms/33.1.77

Subject(s) - mathematics , converse , characterization (materials science) , spectrum (functional analysis) , banach algebra , hausdorff space , algebraic number , pure mathematics , element (criminal law) , algebra over a field , banach space , mathematical analysis , geometry , materials science , physics , quantum mechanics , political science , law , nanotechnology

It is known that if a is an algebraic element of a Banach algebra A , then its spectrum σ( a ) is finite, and there exists γ > 0 such that the Hausdorff distance to spectra of nearby elements satisfies Δ ( σ ( a + x ) , σ ( a ) ) = 0 ( ‖x ‖ γ) as x → 0.We prove that the converse is also true, provided that A is semisimple.

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