Nice connecting paths in connected components of sets of algebraic elements in a Banach algebra

Czechoslovak Mathematical Journal

Jaroslav Zemánek¹  Endre Makai, Jr.² 

[1] Institute of Mathematics, Polish Academy of Sciences, Śniadeckich 8, 00-656 Warsaw, Poland;MTA Alfréd Rényi Institute of Mathematics, Reáltanoda utca 13-15., 1053 Budapest H-1364, Pf. 127, Hungary

关键词: Banach algebra;    $C^*$-algebra;    (self-adjoint) idempotent;    connected component of (self-adjoint) algebraic elements;    (local) pathwise connectedness;    similarity;    analytic path;    polynomial path;    polygonal path;    centre of a ;    Banach algebra;    distance of connected components;   

DOI  :  

学科分类：数学（综合）

来源: Akademie Ved Ceske Republiky

【 摘 要 】

Generalizing earlier results about the set of idempotents in a Banach algebra, or of self-adjoint idempotents in a $C^*$-algebra, we announce constructions of nice connecting paths in the connected components of the set of elements in a Banach algebra, or of self-adjoint elements in a $C^*$-algebra, that satisfy a given polynomial equation, without multiple roots. In particular, we prove that in the Banach algebra case every such non-central element lies on a complex line, all of whose points satisfy the given equation. We also formulate open questions.

【 授权许可】

Unknown