Hecke algebra on homogeneous trees and relations with Toeplitz and Hankel operators

Wysoczański, Janusz

doi:10.1090/S0002-9939-1994-1213871-3

Hecke algebra on homogeneous trees and relations with Toeplitz and Hankel operators
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Proc. Amer. Math. Soc. 122 (1994), 1203-1210 Request permission

Abstract:

We consider the Hecke algebra on homogeneous trees. We prove that it is a maximal abelian subalgebra of some operator algebras if the degree of the tree is greater than 2. There we show the influence of geometry of the tree on that fact. If the degree is 2 (for example, in the case of integers) then we show that operators which commute with the Hecke algebra can be uniquely represented as a sum of Hankel and Toeplitz matrices.

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