The current paper is devoting to studying Branching-Toeplitz operators on the Hilbert space ²(Aq), where Aq is the rooted homogeneous tree of degree q≥ 2. These operators arise from branching-type stationary stochastic processes indexed by rooted tree, and are natural generalizations of Toeplitz operators on classical Hardy spaces. The new findings of this paper are characterizations of basic operator-theoretic properties of branching-Toeplitz operators including boundedness, Brown-Halmos type and Axler-Chang-Sarason-Volberg type results of semi-commutator, spectra, invertibility and Fredholmness.
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Qiu et al. (2024) studied this question.
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