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May 6, 2026Pure and Applied Mathematics JournalOpen Access

On (α, β)–Almost Similar Operators in Hilbert Spaces

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Authors

BABeatrice AdhiamboVWVictor Wanjala

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Overview

This work uncovers the equivalence relation of (α,β)--almost similarity in Hilbert spaces, demonstrating its impact on self-adjoint operators and spectral properties.

Key Points

  • The research aims to define and explore (α,β)--almost similarity and its fundamental properties in the context of operator theory.
  • Introduced the concept of (α,β)--almost similarity for bounded linear operators in Hilbert spaces.
  • Established properties of this new equivalence relation and its spectral implications.
  • Defined (α,β)-𝔗 operators and analyzed their relationship with (α,β)--almost similarity.
  • Demonstrated invariance of spectrum, point spectrum, and approximate point spectrum under (α,β)--almost similarity.
  • Explored connections between similarity, unitary equivalence, and (α,β)--almost similarity for self-adjoint operators.

Cite This Study

Adhiambo et al. (2026) studied this question.

synapsesocial.com/papers/69fa8e6404f884e66b530bf1https://doi.org/10.11648/j.pamj.20261502.13
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  4. 4On Symmetric Aspects of Operator Pair Inequalities in Hilbert Spaces via Pečarić’s Theorem with Applications2025
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