Czechoslovak Mathematical Journal

, Volume 66, Issue 3, pp 821–828 | Cite as

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

  • Endre MakaiJr.
  • Jaroslav Zemánek


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.


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 

MSC 2010

46H20 46L05 


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Copyright information

© Institute of Mathematics of the Academy of Sciences of the Czech Republic, Praha, Czech Republic 2016

Authors and Affiliations

  1. 1.MTA Alfréd Rényi Institute of MathematicsBudapestHungary
  2. 2.Institute of MathematicsPolish Academy of SciencesWarsawPoland

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