On expansive three-isometries

• Autorzy: Suciu Laurian

Identyfikatory

DOI

10.7494/OpMath.2024.44.6.883

• Języki publikacji: EN

Abstrakty

EN

The sub-Brownian 3-isometries in Hilbert spaces are the natural counterparts of the 2-isometries, because all of them have Brownian-type extensions in the sense of J. Agler and M. Stankus. We show that all powers Tn for n ≥ 2 of every expansive 3-isometry T are sub-Brownian, even if T does not have such a property. This fact induces some useful relations between the corresponding covariance operators of T. We analyze two matrix representations of T in order to get some conditions under which T is sub-Brownian, or T admits the Wold-type decomposition in the sense of S. Shimorin. We show that the restriction of T to its range is sub-Brownian of McCullough’s type, and that under some conditions on N(T∗), T itself is sub-Brownian, and it admits the Wold-type decomposition.

Słowa kluczowe

EN

Wold decomposition; 3-isometry; sub-Brownian 3-isometry

• Wydawca: AGH University of Science and Technology Press
• Czasopismo: Opuscula Mathematica
• Rocznik: 2024
• Tom: Vol. 44, no. 6
• Strony: 883--898
• Opis fizyczny: Bibliogr. 10 poz.

Twórcy

autor

Suciu Laurian

• Universitatea Lucian Blaga din Sibiu, Departamentul de Matematica si Informatica, Sibiu, Romania

• https://orcid.org/0000-0002-5675-0519

Bibliografia

• [1] J. Agler, An abstract approach to model theory, [in:] Survey of Some Recent Results in Operator Theory, vol. II, Pitman Res. Notes Math. Ser. 192, 1–23.
• [2] J. Agler, M. Stankus, m-isometric transformations of Hilbert spaces, Integral Equations Operator Theory 21 (1995), 383–429.
• [3] J. Agler, M. Stankus, m-isometric transformations of Hilbert spaces, II, Integral Equations Operator Theory 23 (1995), 1–48.
• [4] J. Agler, M. Stankus, m-isometric transformations of Hilbert spaces, III, Integral Equations Operator Theory 24 (1996), 379–421.
• [5] A. Aleman, The multiplication operator on Hilbert spaces of analytic functions, Habilitationsschrift, Fern Universität, Hagen, 1993.
• [6] A. Crăciunescu, L. Suciu, Brownian extensions in the context of three-isometries, J. Math. Anal. Appl. 529 (2024), 127591.
• [7] J. Kośmider, The Wold-type decomposition for m-isometries, Bull. Malays. Math. Sci. Soc. 44 (2021), 4155–4174.
• [8] W. Majdak, L. Suciu, Brownian type parts of operators in Hilbert spaces, Results Math. 75 (2020), Article 5.
• [9] S. McCullough, SubBrownian operators, J. Oper. Theory 22 (1989), 291–305.
• [10] S. Shimorin, Wold-type decompositions and wandering subspaces for operators close to isometries J. Reine Angew. Math. 531 (2001), 147–189.

Uwagi

Opracowanie rekordu ze środków MEiN, umowa nr SONP/SP/546092/2022 w ramach programu "Społeczna odpowiedzialność nauki" - moduł: Popularyzacja nauki i promocja sportu (2022-2023)