On The Extension of the Toeplitz Algebra by Isometries

2013/02/03 by T. A. Grigoryan, Grigoryan, T. A., E. V. Lipacheva +3
Mathematics · #20M18 #46L05 #47L80 #Advanced Operator Algebra Research #Advanced Topics in Algebra #FOS: Mathematics #Functional Analysis (math.FA) #Holomorphic and Operator Theory #Operator Algebras (math.OA)

paper · pdf · doi:10.48550/arxiv.1302.0475

openalex publication_date 2013/02/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We introduce the notion of π-extension of the semigroup ℤ₊ and study the extensions of the Toeplitz algebras by isometric operators. We show that when the action of the Toeplitz algebra is irreducible all such extensions generate the same algebra, i.e. there are no non-trivial extensions of the Toeplitz algebra. Also we provide the examples of the non-trivial extensions of the Toeplitz algebra in case its representation is reducible.

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