Convexity of the Spectrum of a Multiplication Operator

Authors

  • Seyed Nematolah Khademi
  • Mohammad Taghi Heydari Department of Mathematics, College of Sciences, Yasouj University, Yasouj, Iran

DOI:

https://doi.org/10.30495/jme.v18i0.3051

Keywords:

Invariant subspace, maximal ideal space, Numerical range, State space.

Abstract

Let $F$ be a compact subset  of the complex plane, $m$ be the lebesgue measure and $\nu=m|_F$. If $A$ is the multiplication operator on $L^2(\nu)$ and $C^*(A)$ is the $C^*$-algebra generated by $A$, then $F$ is convex if and only if the pure state space of $C^*(A)$ is convex.

Author Biographies

Seyed Nematolah Khademi

Department of Mathematics, College of Sciences, Yasouj University, Yasouj, 75918 Iran

Mohammad Taghi Heydari, Department of Mathematics, College of Sciences, Yasouj University, Yasouj, Iran

Department of Mathematics, College of Sciences, Yasouj University, Yasouj, 75918 Iran

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Published

2024-08-04

Issue

Vol. 18

Section

Vol. 18, No. 4, (2024)

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