Local spectral properties for operators satisfying A nBA n = U (t)A j U (t) ∗
Abstract
In this paper, we investigate the local spectral properties of bounded linear operators A and B acting on a
Hilbert space H , which satisfy the generalized operator equation
A
nBA n = U (t)A
j U (t)
∗
, t ∈ I ⊆ R,
where U (t) is a strongly continuous family of unitary operators on L . The strong continuity condition means
that for every vector x ∈ L ,
∥U (t)x− U (s)x∥ → 0 as t → s.
We analyze how this time-dependent unitary intertwining affects the transmission of local spectral properties
between A and B. In particular, we establish conditions under which certain local spectral properties of A
are inherited by B, and vice versa. Illustrative examples are provided to demonstrate the applicability of the
developed results and to highlight new phenomena arising from the unitary perturbation parameter t.
Keywords
References
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Details
Primary Language
English
Subjects
Operator Algebras and Functional Analysis
Journal Section
Research Article
Authors
Publication Date
June 25, 2026
Submission Date
October 7, 2025
Acceptance Date
June 2, 2026
Published in Issue
Year 2026 Volume: 2 Number: 1
APA
Wanjala, V. (2026). Local spectral properties for operators satisfying A nBA n = U (t)A j U (t) ∗. Smyrna Journal of Natural and Data Sciences, 2(1), 1-14. https://izlik.org/JA67JY67ER
AMA
1.Wanjala V. Local spectral properties for operators satisfying A nBA n = U (t)A j U (t) ∗. Smyrna Journal of Natural and Data Sciences. 2026;2(1):1-14. https://izlik.org/JA67JY67ER
Chicago
Wanjala, Victor. 2026. “Local Spectral Properties for Operators Satisfying A NBA N = U (t)A J U (t) ∗”. Smyrna Journal of Natural and Data Sciences 2 (1): 1-14. https://izlik.org/JA67JY67ER.
EndNote
Wanjala V (June 1, 2026) Local spectral properties for operators satisfying A nBA n = U (t)A j U (t) ∗. Smyrna Journal of Natural and Data Sciences 2 1 1–14.
IEEE
[1]V. Wanjala, “Local spectral properties for operators satisfying A nBA n = U (t)A j U (t) ∗”, Smyrna Journal of Natural and Data Sciences, vol. 2, no. 1, pp. 1–14, June 2026, [Online]. Available: https://izlik.org/JA67JY67ER
ISNAD
Wanjala, Victor. “Local Spectral Properties for Operators Satisfying A NBA N = U (t)A J U (t) ∗”. Smyrna Journal of Natural and Data Sciences 2/1 (June 1, 2026): 1-14. https://izlik.org/JA67JY67ER.
JAMA
1.Wanjala V. Local spectral properties for operators satisfying A nBA n = U (t)A j U (t) ∗. Smyrna Journal of Natural and Data Sciences. 2026;2:1–14.
MLA
Wanjala, Victor. “Local Spectral Properties for Operators Satisfying A NBA N = U (t)A J U (t) ∗”. Smyrna Journal of Natural and Data Sciences, vol. 2, no. 1, June 2026, pp. 1-14, https://izlik.org/JA67JY67ER.
Vancouver
1.Victor Wanjala. Local spectral properties for operators satisfying A nBA n = U (t)A j U (t) ∗. Smyrna Journal of Natural and Data Sciences [Internet]. 2026 Jun. 1;2(1):1-14. Available from: https://izlik.org/JA67JY67ER