Nilpotent perturbations of m-isometric and m-symmetric tensor products of commuting d-tuples of operators

• Autorzy: Duggal Bhagwati Prashad , Kim Hyoun

Identyfikatory

DOI

10.1515/dema-2023-0146

• Języki publikacji: EN

Abstrakty

EN

If T1 and T2 are commuting d -tuples of Hilbert space operators in B(H)d such that (T∗1⊗I+I⊗T∗2,T1⊗I+I⊗T2) is strictly m -isometric (resp., m -symmetric) for some positive integer m , then there exist a scalar d -tuple λ and positive integers mi , 1≤i≤2 , such that m=m1+2m2−2 , (T∗1+¯λ,T1+λ) is m1 isometric, and T2−λ is m2 -nilpotent (resp., m=m1+m2−1 , (T∗1+¯λ,T1+λ) is m1 -symmetric and (T∗2−¯λ,T2−λ) is m2 symmetric).

Słowa kluczowe

EN

Banach space; left/right multiplication operator; m-isometric and m-symmetric commuting d-tuples of operators; tensor product of operators

• Wydawca: De Gruyter
• Czasopismo: Demonstratio Mathematica
• Rocznik: 2024
• Tom: Vol. 57, nr 1
• Strony: art. no. 20230146
• Opis fizyczny: Bibliogr. 9 poz.

Twórcy

autor

Duggal Bhagwati Prashad

• Faculty of Sciences and Mathematics, University of Niš, P.O. Box 224, 18000 Niš, Serbia

autor

Kim Hyoun

• Department of Mathematics, Incheon National University, Incheon, 22012, Korea

Bibliografia

• [1] J. Gleeson and S. Richter, m-Isometric commuting tuples of operators on a Hilbert space, Integral Equations Operator Theory 56 (2006), no. 2, 181–96.
• [2] O. A. M. Sid Ahmed, M. Cho and J. E. Lee, On m C,( ) -isometric commuting tuples of operators on a Hilbert space, Results Math. 73 (2018), no. 51, 31.
• [3] B. P. Duggal and I. H. Kim, Isometric, symmetric and isosymmetric commuting d-tuples of Banach space operators, Results Math. 78 (2023), 85, 25pp. DOI: https://doi.org/10.1007/s00025-023-01855-0.
• [4] M. Cho and O. A. M. Sid Ahmed, (A,m)-symmetric commuting tuples of operators on a Hilbert space, J. Inequal. Appl. 22 (2019), no. 3, 931–947
• [5] B. P. Duggal, Strict isometric and strict symmetric commuting d-tuples of Banach space operators, Functional Analysis, Approximation and Computation 16 (2024), no. 1, 69–86.
• [6] G. Messaoud, O. B. ElMoctar and O. A. M. Sid Ahmed, Joint A-hyponormality operators in semi-Hilbert spaces, Linear Multilinear Algebra 69 (2021), 2888–2907.
• [7] B. P. Duggal and I. H. Kim, Structure of elementary operators defining m-left invertible, m-self adjoint and related classes of operators, J. Math. Anal. Appl. 495 (2020), 124718.
• [8] C. Gu, Structure of left n-invertible operators and their applications, Studia Math. 226 (2015), 189–211.
• [9] S. Paul and C. Gu, Tensor splitting properties of n-inverse pairs of operators, Studia Math. 238 (2017), 17–36.

Uwagi

Opracowanie rekordu ze środków MNiSW, umowa nr POPUL/SP/0154/2024/02 w ramach programu "Społeczna odpowiedzialność nauki II" - moduł: Popularyzacja nauki (2025).