Tohoku Mathematical Journal
2024
June
SECOND SERIES VOL. 76, NO. 2

Tohoku Math. J.
76 (2024), 153-174

Title BRANCHING-TOEPLITZ OPERATORS ON ROOTED HOMOGENEOUS TREES AND AUTHORED

Author Yanqi Qiu and Zipeng Wang

(Received December 6, 2021, revised August 9, 2022)
Abstract. The current paper is devoting to studying Branching-Toeplitz operators on the Hilbert space $\ell^2(A_q)$, where $A_q$ is the rooted homogeneous tree of degree $q\ge 2$. 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.

Mathematics Subject Classification. Primary 47B35; Secondary 47B65, 15B05, 47D03, 46N30.
Key words and phrases. Branching-Toeplitz operators, full Fock spaces, homogeneous trees, free semi-groups.

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