We study Birkhoff-James orthogonality and isosceles orthogonality of bounded linear operators between Hilbert spaces and Banach spaces. We explore Birkhoff-James orthogonality of bounded linear operators in light of a new notion introduced by us and also discuss some of the possible applications in this regard. We also study isosceles orthogonality of bounded (positive) linear operators on a Hilbert space and some of the related properties, including that of operators having disjoint support. We further explore the relations between Birkhoff-James orthogonality and isosceles orthogonality in a general Banach space.

中文翻译：

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有界线性算子的正交性研究

我们研究了希尔伯特空间和巴拿赫空间之间有界线性算子的 Birkhoff-James 正交性和等腰正交性。我们根据我们引入的新概念探索了有界线性算子的 Birkhoff-James 正交性，并讨论了这方面的一些可能应用。我们还研究了希尔伯特空间上有界（正）线性算子的等腰正交性和一些相关属性，包括具有不相交支持的算子的属性。我们进一步探讨了一般 Banach 空间中 Birkhoff-James 正交性和等腰正交性之间的关系。