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<p>In this paper, we characterize the Singer-type orthogonality of bounded linear operators using the concepts of norm attainment set and disjoint support in Hilbert spaces. Also, we introduce a well-defined Singer-type angle using Singer-type orthogonality. We establish some results regarding the angle preservation of mappings for a linear operator. We discuss the relationship of the Singer-type angle with the Euclidean, isosceles, and Thy angles. Furthermore, we discuss its geometrical properties by defining acute, obtuse, and right angles in the setting of normed spaces. Some non-trivial examples are also provided to support the results.</p>

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A new characterization of the Singer-type orthogonality

  • 期刊论文

  • 发表日期：

    2025年11月29日

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  • Kallal Pal,
  • Sumit Chandok

摘要

In this paper, we characterize the Singer-type orthogonality of bounded linear operators using the concepts of norm attainment set and disjoint support in Hilbert spaces. Also, we introduce a well-defined Singer-type angle using Singer-type orthogonality. We establish some results regarding the angle preservation of mappings for a linear operator. We discuss the relationship of the Singer-type angle with the Euclidean, isosceles, and Thy angles. Furthermore, we discuss its geometrical properties by defining acute, obtuse, and right angles in the setting of normed spaces. Some non-trivial examples are also provided to support the results.