Fil: Bottazzi, Tamara P. Universidad Nacional de Río Negro. LaPAC. Río Negro, Argentina.Fil: Conde, Cristian. Instituto Argentino de Matemática “Alberto P. Calderón". Buenos Aires, Argentina.Fil: Conde, Cristian. Instituto de Ciencias, Universidad Nacional de Gral. Sarmiento. Los Polvorines, Argentina.Fil: Sain, Debmalya. Indian Institute of Science, Bengaluru, Karnataka, IndiaWe 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. Birkhoff-James orthogonality and isosceles orthogonality and norm attainment set and disjoint supporttrueEstudiamos las ortogonalidades de tipo Birkhoff-James orthogonality e isósceles entre operadores lineales y acotados de espacios de Hilbert y Banach.