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Far East Journal of Mathematical Sciences (FJMS)

Abstract:
Let A be a uniform algebra on X and P be a set of all probability measures on X. For each m in P,

is the closure of A in

and

is a Toeplitz operator on

for a continuous function f on X. In this paper we study the invertibility and the spectrum of

We show that if

is invertible, then the index of f is zero and if the converse is true for an arbitrary continuous function f, then A is a Dirichlet algebra on X. Moreover we study the spectrum
of

Keywords and phrases: Toeplitz operator, uniform algebra, spectrum, convex-hull, index.

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P-ISSN: 0972-0871

E-ISSN: 2584-1246

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